Properties

Label 656.1
Level 656
Weight 1
Dimension 16
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 26880
Trace bound 4

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Defining parameters

Level: \( N \) = \( 656 = 2^{4} \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(26880\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(656))\).

Total New Old
Modular forms 655 192 463
Cusp forms 95 16 79
Eisenstein series 560 176 384

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q - 2 q^{4} + 2 q^{5} + 4 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{4} + 2 q^{5} + 4 q^{9} + 2 q^{10} + 2 q^{16} + 2 q^{18} - 2 q^{20} + 4 q^{25} - 2 q^{37} - 2 q^{40} - 4 q^{41} - 2 q^{43} - 10 q^{45} + 6 q^{49} + 2 q^{50} - 8 q^{57} + 2 q^{59} - 2 q^{61} - 4 q^{62} - 2 q^{64} - 10 q^{65} - 2 q^{72} - 2 q^{74} - 8 q^{77} + 2 q^{80} - 8 q^{81} - 2 q^{82} + 2 q^{83} - 10 q^{85} + 2 q^{86} + 2 q^{90} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(656))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
656.1.c \(\chi_{656}(327, \cdot)\) None 0 1
656.1.e \(\chi_{656}(575, \cdot)\) None 0 1
656.1.f \(\chi_{656}(247, \cdot)\) None 0 1
656.1.h \(\chi_{656}(655, \cdot)\) 656.1.h.a 4 1
656.1.j \(\chi_{656}(91, \cdot)\) None 0 2
656.1.k \(\chi_{656}(255, \cdot)\) 656.1.k.a 2 2
656.1.m \(\chi_{656}(163, \cdot)\) 656.1.m.a 2 2
656.1.p \(\chi_{656}(83, \cdot)\) None 0 2
656.1.q \(\chi_{656}(583, \cdot)\) None 0 2
656.1.s \(\chi_{656}(155, \cdot)\) None 0 2
656.1.w \(\chi_{656}(85, \cdot)\) None 0 4
656.1.x \(\chi_{656}(137, \cdot)\) None 0 4
656.1.y \(\chi_{656}(161, \cdot)\) None 0 4
656.1.bc \(\chi_{656}(413, \cdot)\) None 0 4
656.1.bd \(\chi_{656}(223, \cdot)\) None 0 4
656.1.bf \(\chi_{656}(23, \cdot)\) None 0 4
656.1.bh \(\chi_{656}(31, \cdot)\) None 0 4
656.1.bj \(\chi_{656}(119, \cdot)\) None 0 4
656.1.bk \(\chi_{656}(115, \cdot)\) None 0 8
656.1.bn \(\chi_{656}(39, \cdot)\) None 0 8
656.1.bo \(\chi_{656}(51, \cdot)\) None 0 8
656.1.br \(\chi_{656}(107, \cdot)\) None 0 8
656.1.bt \(\chi_{656}(143, \cdot)\) 656.1.bt.a 8 8
656.1.bv \(\chi_{656}(43, \cdot)\) None 0 8
656.1.bw \(\chi_{656}(13, \cdot)\) None 0 16
656.1.ca \(\chi_{656}(17, \cdot)\) None 0 16
656.1.cb \(\chi_{656}(89, \cdot)\) None 0 16
656.1.cc \(\chi_{656}(53, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(656))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(656)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 2}\)