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Properties

Label 2624.1
Level 2624
Weight 1
Dimension 111
Nonzero newspaces 12
Newform subspaces 17
Sturm bound 430080
Trace bound 13

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Defining parameters

Level: \( N \) = \( 2624 = 2^{6} \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 17 \)
Sturm bound: \(430080\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2624))\).

Total New Old
Modular forms 3280 969 2311
Cusp forms 400 111 289
Eisenstein series 2880 858 2022

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 95 0 0 16

Trace form

\( 111 q + 4 q^{5} + 13 q^{9} + O(q^{10}) \) \( 111 q + 4 q^{5} + 13 q^{9} + 2 q^{13} - 6 q^{17} + 8 q^{20} + 4 q^{21} + 11 q^{25} + 2 q^{29} - 16 q^{33} - 8 q^{40} + q^{41} + 2 q^{43} + 8 q^{45} - 8 q^{46} + 19 q^{49} + 2 q^{53} + 4 q^{57} - 2 q^{59} + 4 q^{61} - 12 q^{65} - 2 q^{73} + 8 q^{74} + 4 q^{77} - q^{81} - 2 q^{83} + 4 q^{85} - 6 q^{89} + 8 q^{90} + 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2624))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2624.1.c \(\chi_{2624}(1311, \cdot)\) None 0 1
2624.1.e \(\chi_{2624}(575, \cdot)\) None 0 1
2624.1.f \(\chi_{2624}(1887, \cdot)\) None 0 1
2624.1.h \(\chi_{2624}(2623, \cdot)\) 2624.1.h.a 1 1
2624.1.h.b 2
2624.1.h.c 4
2624.1.j \(\chi_{2624}(911, \cdot)\) None 0 2
2624.1.k \(\chi_{2624}(255, \cdot)\) 2624.1.k.a 2 2
2624.1.m \(\chi_{2624}(655, \cdot)\) 2624.1.m.a 2 2
2624.1.p \(\chi_{2624}(1231, \cdot)\) None 0 2
2624.1.q \(\chi_{2624}(1567, \cdot)\) None 0 2
2624.1.s \(\chi_{2624}(975, \cdot)\) None 0 2
2624.1.w \(\chi_{2624}(137, \cdot)\) None 0 4
2624.1.y \(\chi_{2624}(273, \cdot)\) None 0 4
2624.1.z \(\chi_{2624}(647, \cdot)\) None 0 4
2624.1.bb \(\chi_{2624}(793, \cdot)\) None 0 4
2624.1.bd \(\chi_{2624}(489, \cdot)\) None 0 4
2624.1.bg \(\chi_{2624}(327, \cdot)\) None 0 4
2624.1.bh \(\chi_{2624}(161, \cdot)\) 2624.1.bh.a 4 4
2624.1.bh.b 4
2624.1.bi \(\chi_{2624}(577, \cdot)\) 2624.1.bi.a 4 4
2624.1.bl \(\chi_{2624}(247, \cdot)\) None 0 4
2624.1.bn \(\chi_{2624}(583, \cdot)\) None 0 4
2624.1.bq \(\chi_{2624}(1233, \cdot)\) None 0 4
2624.1.br \(\chi_{2624}(1145, \cdot)\) None 0 4
2624.1.bt \(\chi_{2624}(447, \cdot)\) 2624.1.bt.a 4 4
2624.1.bv \(\chi_{2624}(31, \cdot)\) None 0 4
2624.1.bx \(\chi_{2624}(127, \cdot)\) 2624.1.bx.a 4 4
2624.1.bz \(\chi_{2624}(223, \cdot)\) 2624.1.bz.a 8 4
2624.1.bz.b 8
2624.1.cb \(\chi_{2624}(413, \cdot)\) None 0 8
2624.1.cc \(\chi_{2624}(91, \cdot)\) None 0 8
2624.1.ci \(\chi_{2624}(83, \cdot)\) None 0 8
2624.1.cj \(\chi_{2624}(163, \cdot)\) 2624.1.cj.a 8 8
2624.1.ck \(\chi_{2624}(85, \cdot)\) None 0 8
2624.1.cl \(\chi_{2624}(301, \cdot)\) None 0 8
2624.1.cn \(\chi_{2624}(155, \cdot)\) None 0 8
2624.1.cp \(\chi_{2624}(437, \cdot)\) None 0 8
2624.1.cq \(\chi_{2624}(815, \cdot)\) None 0 8
2624.1.ct \(\chi_{2624}(159, \cdot)\) None 0 8
2624.1.cu \(\chi_{2624}(303, \cdot)\) None 0 8
2624.1.cx \(\chi_{2624}(271, \cdot)\) None 0 8
2624.1.cz \(\chi_{2624}(1023, \cdot)\) 2624.1.cz.a 8 8
2624.1.db \(\chi_{2624}(143, \cdot)\) None 0 8
2624.1.dc \(\chi_{2624}(217, \cdot)\) None 0 16
2624.1.de \(\chi_{2624}(753, \cdot)\) None 0 16
2624.1.dh \(\chi_{2624}(39, \cdot)\) None 0 16
2624.1.dj \(\chi_{2624}(233, \cdot)\) None 0 16
2624.1.dl \(\chi_{2624}(345, \cdot)\) None 0 16
2624.1.dn \(\chi_{2624}(119, \cdot)\) None 0 16
2624.1.dq \(\chi_{2624}(65, \cdot)\) 2624.1.dq.a 16 16
2624.1.dr \(\chi_{2624}(97, \cdot)\) 2624.1.dr.a 16 16
2624.1.dr.b 16
2624.1.ds \(\chi_{2624}(23, \cdot)\) None 0 16
2624.1.dv \(\chi_{2624}(87, \cdot)\) None 0 16
2624.1.dw \(\chi_{2624}(17, \cdot)\) None 0 16
2624.1.dz \(\chi_{2624}(89, \cdot)\) None 0 16
2624.1.ea \(\chi_{2624}(13, \cdot)\) None 0 32
2624.1.ec \(\chi_{2624}(43, \cdot)\) None 0 32
2624.1.ee \(\chi_{2624}(53, \cdot)\) None 0 32
2624.1.ef \(\chi_{2624}(69, \cdot)\) None 0 32
2624.1.eg \(\chi_{2624}(107, \cdot)\) None 0 32
2624.1.eh \(\chi_{2624}(51, \cdot)\) None 0 32
2624.1.en \(\chi_{2624}(115, \cdot)\) None 0 32
2624.1.eo \(\chi_{2624}(29, \cdot)\) None 0 32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2624))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2624)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(656))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1312))\)\(^{\oplus 2}\)