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Properties

Label 2640.1
Level 2640
Weight 1
Dimension 24
Nonzero newspaces 2
Newform subspaces 12
Sturm bound 368640
Trace bound 15

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Defining parameters

Level: \( N \) = \( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 12 \)
Sturm bound: \(368640\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2640))\).

Total New Old
Modular forms 4992 512 4480
Cusp forms 512 24 488
Eisenstein series 4480 488 3992

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24 q + O(q^{10}) \) \( 24 q + 6 q^{15} + 6 q^{27} - 6 q^{45} + 12 q^{49} - 12 q^{69} - 6 q^{75} - 6 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2640))\)

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
2640.1.b \(\chi_{2640}(1319, \cdot)\) None 0 1
2640.1.c \(\chi_{2640}(241, \cdot)\) None 0 1
2640.1.h \(\chi_{2640}(2311, \cdot)\) None 0 1
2640.1.i \(\chi_{2640}(1409, \cdot)\) None 0 1
2640.1.l \(\chi_{2640}(2639, \cdot)\) 2640.1.l.a 1 1
2640.1.l.b 1
2640.1.l.c 1
2640.1.l.d 1
2640.1.l.e 2
2640.1.l.f 2
2640.1.l.g 2
2640.1.l.h 2
2640.1.m \(\chi_{2640}(1561, \cdot)\) None 0 1
2640.1.n \(\chi_{2640}(991, \cdot)\) None 0 1
2640.1.o \(\chi_{2640}(89, \cdot)\) None 0 1
2640.1.r \(\chi_{2640}(2201, \cdot)\) None 0 1
2640.1.s \(\chi_{2640}(1519, \cdot)\) None 0 1
2640.1.x \(\chi_{2640}(2089, \cdot)\) None 0 1
2640.1.y \(\chi_{2640}(2111, \cdot)\) None 0 1
2640.1.bb \(\chi_{2640}(881, \cdot)\) None 0 1
2640.1.bc \(\chi_{2640}(199, \cdot)\) None 0 1
2640.1.bd \(\chi_{2640}(769, \cdot)\) None 0 1
2640.1.be \(\chi_{2640}(791, \cdot)\) None 0 1
2640.1.bg \(\chi_{2640}(859, \cdot)\) None 0 2
2640.1.bj \(\chi_{2640}(221, \cdot)\) None 0 2
2640.1.bk \(\chi_{2640}(131, \cdot)\) None 0 2
2640.1.bn \(\chi_{2640}(109, \cdot)\) None 0 2
2640.1.bp \(\chi_{2640}(2003, \cdot)\) None 0 2
2640.1.br \(\chi_{2640}(43, \cdot)\) None 0 2
2640.1.bs \(\chi_{2640}(1453, \cdot)\) None 0 2
2640.1.bu \(\chi_{2640}(1253, \cdot)\) None 0 2
2640.1.bw \(\chi_{2640}(23, \cdot)\) None 0 2
2640.1.bz \(\chi_{2640}(1057, \cdot)\) None 0 2
2640.1.ca \(\chi_{2640}(703, \cdot)\) None 0 2
2640.1.cd \(\chi_{2640}(857, \cdot)\) None 0 2
2640.1.ce \(\chi_{2640}(967, \cdot)\) None 0 2
2640.1.ch \(\chi_{2640}(593, \cdot)\) 2640.1.ch.a 2 2
2640.1.ch.b 2
2640.1.ch.c 4
2640.1.ch.d 4
2640.1.ci \(\chi_{2640}(287, \cdot)\) None 0 2
2640.1.cl \(\chi_{2640}(793, \cdot)\) None 0 2
2640.1.cn \(\chi_{2640}(1363, \cdot)\) None 0 2
2640.1.cp \(\chi_{2640}(683, \cdot)\) None 0 2
2640.1.cq \(\chi_{2640}(197, \cdot)\) None 0 2
2640.1.cs \(\chi_{2640}(133, \cdot)\) None 0 2
2640.1.cv \(\chi_{2640}(901, \cdot)\) None 0 2
2640.1.cw \(\chi_{2640}(659, \cdot)\) None 0 2
2640.1.cz \(\chi_{2640}(749, \cdot)\) None 0 2
2640.1.da \(\chi_{2640}(331, \cdot)\) None 0 2
2640.1.de \(\chi_{2640}(1009, \cdot)\) None 0 4
2640.1.df \(\chi_{2640}(1031, \cdot)\) None 0 4
2640.1.dg \(\chi_{2640}(401, \cdot)\) None 0 4
2640.1.dh \(\chi_{2640}(1159, \cdot)\) None 0 4
2640.1.dk \(\chi_{2640}(409, \cdot)\) None 0 4
2640.1.dl \(\chi_{2640}(431, \cdot)\) None 0 4
2640.1.dq \(\chi_{2640}(521, \cdot)\) None 0 4
2640.1.dr \(\chi_{2640}(559, \cdot)\) None 0 4
2640.1.du \(\chi_{2640}(31, \cdot)\) None 0 4
2640.1.dv \(\chi_{2640}(1049, \cdot)\) None 0 4
2640.1.dw \(\chi_{2640}(239, \cdot)\) None 0 4
2640.1.dx \(\chi_{2640}(601, \cdot)\) None 0 4
2640.1.ea \(\chi_{2640}(631, \cdot)\) None 0 4
2640.1.eb \(\chi_{2640}(449, \cdot)\) None 0 4
2640.1.eg \(\chi_{2640}(359, \cdot)\) None 0 4
2640.1.eh \(\chi_{2640}(481, \cdot)\) None 0 4
2640.1.ei \(\chi_{2640}(269, \cdot)\) None 0 8
2640.1.el \(\chi_{2640}(91, \cdot)\) None 0 8
2640.1.em \(\chi_{2640}(61, \cdot)\) None 0 8
2640.1.ep \(\chi_{2640}(299, \cdot)\) None 0 8
2640.1.er \(\chi_{2640}(157, \cdot)\) None 0 8
2640.1.et \(\chi_{2640}(173, \cdot)\) None 0 8
2640.1.eu \(\chi_{2640}(203, \cdot)\) None 0 8
2640.1.ew \(\chi_{2640}(403, \cdot)\) None 0 8
2640.1.ey \(\chi_{2640}(313, \cdot)\) None 0 8
2640.1.fb \(\chi_{2640}(47, \cdot)\) None 0 8
2640.1.fc \(\chi_{2640}(17, \cdot)\) None 0 8
2640.1.ff \(\chi_{2640}(7, \cdot)\) None 0 8
2640.1.fg \(\chi_{2640}(233, \cdot)\) None 0 8
2640.1.fj \(\chi_{2640}(127, \cdot)\) None 0 8
2640.1.fk \(\chi_{2640}(97, \cdot)\) None 0 8
2640.1.fn \(\chi_{2640}(647, \cdot)\) None 0 8
2640.1.fp \(\chi_{2640}(293, \cdot)\) None 0 8
2640.1.fr \(\chi_{2640}(37, \cdot)\) None 0 8
2640.1.fs \(\chi_{2640}(283, \cdot)\) None 0 8
2640.1.fu \(\chi_{2640}(323, \cdot)\) None 0 8
2640.1.fx \(\chi_{2640}(371, \cdot)\) None 0 8
2640.1.fy \(\chi_{2640}(349, \cdot)\) None 0 8
2640.1.gb \(\chi_{2640}(379, \cdot)\) None 0 8
2640.1.gc \(\chi_{2640}(581, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2640))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2640)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1320))\)\(^{\oplus 2}\)