Properties

Label 656.1.h
Level $656$
Weight $1$
Character orbit 656.h
Rep. character $\chi_{656}(655,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 656 = 2^{4} \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 656.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(656, [\chi])\).

Total New Old
Modular forms 19 4 15
Cusp forms 13 4 9
Eisenstein series 6 0 6

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{9} + 4 q^{25} - 4 q^{41} - 8 q^{45} + 4 q^{49} - 8 q^{57} - 8 q^{77} + 4 q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(656, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
656.1.h.a $4$ $0.327$ \(\Q(\zeta_{16})^+\) $D_{8}$ \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(656, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(656, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 3}\)