Properties

Label 2600.1
Level 2600
Weight 1
Dimension 108
Nonzero newspaces 14
Newform subspaces 31
Sturm bound 403200
Trace bound 29

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Defining parameters

Level: \( N \) = \( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 14 \)
Newform subspaces: \( 31 \)
Sturm bound: \(403200\)
Trace bound: \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2600))\).

Total New Old
Modular forms 4586 1010 3576
Cusp forms 554 108 446
Eisenstein series 4032 902 3130

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 100 0 8 0

Trace form

\( 108 q + 2 q^{3} + 4 q^{4} - 4 q^{6} + 6 q^{9} + O(q^{10}) \) \( 108 q + 2 q^{3} + 4 q^{4} - 4 q^{6} + 6 q^{9} - 12 q^{11} + 2 q^{12} + 2 q^{14} - 12 q^{16} + 6 q^{17} - 8 q^{19} - 8 q^{21} + 4 q^{22} - 4 q^{23} - 4 q^{24} - 14 q^{27} - 12 q^{30} - 4 q^{31} - 12 q^{35} - 2 q^{36} + 4 q^{38} - 4 q^{39} - 8 q^{41} - 14 q^{42} + 2 q^{43} + 4 q^{44} - 4 q^{46} + 2 q^{48} + 6 q^{49} - 6 q^{51} + 22 q^{56} + 4 q^{59} + 8 q^{61} + 44 q^{62} + 4 q^{64} - 2 q^{68} + 4 q^{71} - 10 q^{74} - 12 q^{75} + 32 q^{76} + 2 q^{78} - 32 q^{81} + 4 q^{86} - 4 q^{88} - 4 q^{89} + 48 q^{90} + 2 q^{91} - 4 q^{92} - 2 q^{94} + 4 q^{96} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2600))\)

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
2600.1.b \(\chi_{2600}(1299, \cdot)\) 2600.1.b.a 2 1
2600.1.b.b 2
2600.1.c \(\chi_{2600}(1951, \cdot)\) None 0 1
2600.1.h \(\chi_{2600}(1899, \cdot)\) None 0 1
2600.1.i \(\chi_{2600}(1351, \cdot)\) None 0 1
2600.1.l \(\chi_{2600}(2599, \cdot)\) None 0 1
2600.1.m \(\chi_{2600}(651, \cdot)\) None 0 1
2600.1.n \(\chi_{2600}(599, \cdot)\) None 0 1
2600.1.o \(\chi_{2600}(51, \cdot)\) 2600.1.o.a 1 1
2600.1.o.b 1
2600.1.o.c 1
2600.1.o.d 1
2600.1.o.e 2
2600.1.o.f 2
2600.1.r \(\chi_{2600}(2101, \cdot)\) 2600.1.r.a 4 2
2600.1.u \(\chi_{2600}(2049, \cdot)\) 2600.1.u.a 2 2
2600.1.u.b 2
2600.1.v \(\chi_{2600}(343, \cdot)\) None 0 2
2600.1.x \(\chi_{2600}(307, \cdot)\) 2600.1.x.a 2 2
2600.1.x.b 2
2600.1.z \(\chi_{2600}(857, \cdot)\) None 0 2
2600.1.ba \(\chi_{2600}(157, \cdot)\) None 0 2
2600.1.bf \(\chi_{2600}(1457, \cdot)\) None 0 2
2600.1.bg \(\chi_{2600}(493, \cdot)\) 2600.1.bg.a 4 2
2600.1.bi \(\chi_{2600}(2007, \cdot)\) None 0 2
2600.1.bk \(\chi_{2600}(707, \cdot)\) 2600.1.bk.a 2 2
2600.1.bk.b 2
2600.1.bl \(\chi_{2600}(801, \cdot)\) 2600.1.bl.a 2 2
2600.1.bl.b 2
2600.1.bo \(\chi_{2600}(749, \cdot)\) None 0 2
2600.1.br \(\chi_{2600}(251, \cdot)\) 2600.1.br.a 2 2
2600.1.br.b 2
2600.1.bs \(\chi_{2600}(399, \cdot)\) None 0 2
2600.1.bt \(\chi_{2600}(451, \cdot)\) 2600.1.bt.a 4 2
2600.1.bu \(\chi_{2600}(199, \cdot)\) None 0 2
2600.1.bx \(\chi_{2600}(751, \cdot)\) None 0 2
2600.1.by \(\chi_{2600}(1699, \cdot)\) None 0 2
2600.1.cd \(\chi_{2600}(1751, \cdot)\) None 0 2
2600.1.ce \(\chi_{2600}(699, \cdot)\) None 0 2
2600.1.cf \(\chi_{2600}(131, \cdot)\) None 0 4
2600.1.cg \(\chi_{2600}(519, \cdot)\) None 0 4
2600.1.ck \(\chi_{2600}(571, \cdot)\) 2600.1.ck.a 4 4
2600.1.ck.b 4
2600.1.ck.c 8
2600.1.ck.d 8
2600.1.cl \(\chi_{2600}(79, \cdot)\) None 0 4
2600.1.co \(\chi_{2600}(391, \cdot)\) None 0 4
2600.1.cp \(\chi_{2600}(259, \cdot)\) 2600.1.cp.a 8 4
2600.1.cp.b 16
2600.1.cq \(\chi_{2600}(311, \cdot)\) None 0 4
2600.1.cr \(\chi_{2600}(339, \cdot)\) None 0 4
2600.1.cu \(\chi_{2600}(149, \cdot)\) None 0 4
2600.1.cx \(\chi_{2600}(201, \cdot)\) None 0 4
2600.1.cy \(\chi_{2600}(843, \cdot)\) 2600.1.cy.a 4 4
2600.1.cy.b 4
2600.1.da \(\chi_{2600}(943, \cdot)\) None 0 4
2600.1.de \(\chi_{2600}(693, \cdot)\) None 0 4
2600.1.df \(\chi_{2600}(393, \cdot)\) None 0 4
2600.1.dg \(\chi_{2600}(757, \cdot)\) None 0 4
2600.1.dh \(\chi_{2600}(257, \cdot)\) None 0 4
2600.1.dl \(\chi_{2600}(643, \cdot)\) 2600.1.dl.a 4 4
2600.1.dl.b 4
2600.1.dn \(\chi_{2600}(7, \cdot)\) None 0 4
2600.1.do \(\chi_{2600}(249, \cdot)\) None 0 4
2600.1.dr \(\chi_{2600}(301, \cdot)\) None 0 4
2600.1.dt \(\chi_{2600}(109, \cdot)\) None 0 8
2600.1.dw \(\chi_{2600}(161, \cdot)\) None 0 8
2600.1.dy \(\chi_{2600}(83, \cdot)\) None 0 8
2600.1.ea \(\chi_{2600}(47, \cdot)\) None 0 8
2600.1.eb \(\chi_{2600}(77, \cdot)\) None 0 8
2600.1.ec \(\chi_{2600}(313, \cdot)\) None 0 8
2600.1.eh \(\chi_{2600}(53, \cdot)\) None 0 8
2600.1.ei \(\chi_{2600}(233, \cdot)\) None 0 8
2600.1.ej \(\chi_{2600}(187, \cdot)\) None 0 8
2600.1.el \(\chi_{2600}(447, \cdot)\) None 0 8
2600.1.en \(\chi_{2600}(369, \cdot)\) None 0 8
2600.1.eq \(\chi_{2600}(21, \cdot)\) None 0 8
2600.1.et \(\chi_{2600}(139, \cdot)\) None 0 8
2600.1.eu \(\chi_{2600}(231, \cdot)\) None 0 8
2600.1.ev \(\chi_{2600}(179, \cdot)\) None 0 8
2600.1.ew \(\chi_{2600}(191, \cdot)\) None 0 8
2600.1.ez \(\chi_{2600}(159, \cdot)\) None 0 8
2600.1.fa \(\chi_{2600}(491, \cdot)\) None 0 8
2600.1.fe \(\chi_{2600}(439, \cdot)\) None 0 8
2600.1.ff \(\chi_{2600}(211, \cdot)\) None 0 8
2600.1.fg \(\chi_{2600}(141, \cdot)\) None 0 16
2600.1.fj \(\chi_{2600}(89, \cdot)\) None 0 16
2600.1.fl \(\chi_{2600}(63, \cdot)\) None 0 16
2600.1.fn \(\chi_{2600}(67, \cdot)\) None 0 16
2600.1.fq \(\chi_{2600}(17, \cdot)\) None 0 16
2600.1.fr \(\chi_{2600}(133, \cdot)\) None 0 16
2600.1.fs \(\chi_{2600}(113, \cdot)\) None 0 16
2600.1.ft \(\chi_{2600}(173, \cdot)\) None 0 16
2600.1.fw \(\chi_{2600}(167, \cdot)\) None 0 16
2600.1.fy \(\chi_{2600}(123, \cdot)\) None 0 16
2600.1.ga \(\chi_{2600}(41, \cdot)\) None 0 16
2600.1.gd \(\chi_{2600}(189, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2600))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2600)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1300))\)\(^{\oplus 2}\)