# On ℓ-adic representations for a space of noncongruence cuspforms

@inproceedings{Hoffman2010OnR, title={On ℓ-adic representations for a space of noncongruence cuspforms}, author={J. William Hoffman and Ling Long and Helena A. Verrill}, year={2010} }

This paper is concerned with a compatible family of 4-dimensional l-adic representations ρl of GQ := Gal(Q/Q) attached to the space of weight-3 cuspforms S3(Γ) on a noncongruence subgroup Γ ⊂ SL2(Z). For this representation we prove that:
1.
It is automorphic: the L-function L(s,ρl∨) agrees with the L-function for an automorphic form for GL4(AQ), where ρl∨ is the dual of ρl.
2.
For each prime p≥5 there is a basis hp = {hp+, hp-} of S3(Γ) whose expansion coefficients satisfy 3-term Atkin…

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