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In this paper we construct five endoscopic lifts $\\Pi_i,0\\le i\\le 4$ from two elliptic modular forms $f\\otimes\\chi^i$ of weight 2 and $g\\otimes\\chi^i$ of weight 4 with complex multiplication by $Q(\\sqrt{-11})$ such that ${\\Pi_i}_\\infty$ gives a non-holomorphic differential form on $A^{lev}_{11}$ for each $i$. Then the spinor L-function is of form $L(f\\otimes\\chi^i,s-1)L(g\\otimes\\chi^i,s)$ such that $L(g\\otimes\\chi^i,s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.2052","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-12T06:24:32Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bcabc2ba44a91b431b502e3aeed721fb9910bf9354ccfdd99c778e004220d53c","abstract_canon_sha256":"a5e1397f0ad5b260163af2a9a84271509332b842bfdc78dc66636881f6931b6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:11.294152Z","signature_b64":"iholBc2MusKfuoA8B23rhLsUYJFDcWQRO+llWJC6zsZUkSHo2PD7MOzp6sedJXW+rvWxiGMzz0sSc3YFWzH1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73cdb039c55e4aa91624e6553d1e725fe1111924593d08998ac0b22baf3735fa","last_reissued_at":"2026-05-18T03:41:11.293730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:11.293730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Endoscopic lifts to the Siegel modular threefold related to Klein's cubic threefold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Takeo Okazaki, Takuya Yamauchi","submitted_at":"2010-08-12T06:24:32Z","abstract_excerpt":"Let $A^{lev}_{11}$ be the moduli space of (1,11)-polarized abelian surfaces with level structure of canonical type. 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