Theta cycles of weight k < p modular forms modulo p² are exactly determined on the initial segment of length p, with exact values or nontrivial bounds on p-2 further segments of length p-k+1, covering 50% exactly and 100% with bounds asymptotically.
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Theta Cycles of Modular Forms Modulo $p^2$
Theta cycles of weight k < p modular forms modulo p² are exactly determined on the initial segment of length p, with exact values or nontrivial bounds on p-2 further segments of length p-k+1, covering 50% exactly and 100% with bounds asymptotically.