Properties

Label 2475.1
Level 2475
Weight 1
Dimension 111
Nonzero newspaces 10
Newform subspaces 18
Sturm bound 432000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 18 \)
Sturm bound: \(432000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2475))\).

Total New Old
Modular forms 4724 1772 2952
Cusp forms 244 111 133
Eisenstein series 4480 1661 2819

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 111 0 0 0

Trace form

\( 111 q - q^{3} - 4 q^{4} + 7 q^{9} + O(q^{10}) \) \( 111 q - q^{3} - 4 q^{4} + 7 q^{9} + 7 q^{12} - 22 q^{16} + 6 q^{20} + 8 q^{23} + 8 q^{25} + 2 q^{27} - q^{31} - 14 q^{33} + 8 q^{34} + 2 q^{36} + 12 q^{37} - 11 q^{44} + 11 q^{47} - 14 q^{48} - 4 q^{49} + 8 q^{53} + 6 q^{55} - 31 q^{59} - 16 q^{60} + 7 q^{64} - q^{67} + 6 q^{69} + 4 q^{75} - q^{81} + 2 q^{89} - 8 q^{91} - 22 q^{92} - 11 q^{93} - q^{97} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2475))\)

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
2475.1.b \(\chi_{2475}(901, \cdot)\) 2475.1.b.a 1 1
2475.1.b.b 2
2475.1.b.c 2
2475.1.e \(\chi_{2475}(1376, \cdot)\) None 0 1
2475.1.g \(\chi_{2475}(1574, \cdot)\) None 0 1
2475.1.h \(\chi_{2475}(1099, \cdot)\) None 0 1
2475.1.j \(\chi_{2475}(793, \cdot)\) None 0 2
2475.1.m \(\chi_{2475}(593, \cdot)\) 2475.1.m.a 8 2
2475.1.m.b 8
2475.1.t \(\chi_{2475}(274, \cdot)\) 2475.1.t.a 4 2
2475.1.v \(\chi_{2475}(749, \cdot)\) None 0 2
2475.1.x \(\chi_{2475}(551, \cdot)\) None 0 2
2475.1.y \(\chi_{2475}(76, \cdot)\) 2475.1.y.a 2 2
2475.1.y.b 4
2475.1.bb \(\chi_{2475}(71, \cdot)\) None 0 4
2475.1.bc \(\chi_{2475}(316, \cdot)\) None 0 4
2475.1.be \(\chi_{2475}(89, \cdot)\) None 0 4
2475.1.bg \(\chi_{2475}(424, \cdot)\) None 0 4
2475.1.bh \(\chi_{2475}(19, \cdot)\) None 0 4
2475.1.bi \(\chi_{2475}(469, \cdot)\) None 0 4
2475.1.bj \(\chi_{2475}(514, \cdot)\) None 0 4
2475.1.bk \(\chi_{2475}(269, \cdot)\) None 0 4
2475.1.bm \(\chi_{2475}(179, \cdot)\) None 0 4
2475.1.bo \(\chi_{2475}(1169, \cdot)\) None 0 4
2475.1.bp \(\chi_{2475}(224, \cdot)\) None 0 4
2475.1.bs \(\chi_{2475}(109, \cdot)\) 2475.1.bs.a 4 4
2475.1.bu \(\chi_{2475}(406, \cdot)\) 2475.1.bu.a 4 4
2475.1.bv \(\chi_{2475}(971, \cdot)\) None 0 4
2475.1.bx \(\chi_{2475}(26, \cdot)\) None 0 4
2475.1.by \(\chi_{2475}(521, \cdot)\) None 0 4
2475.1.cb \(\chi_{2475}(746, \cdot)\) None 0 4
2475.1.ce \(\chi_{2475}(46, \cdot)\) None 0 4
2475.1.ch \(\chi_{2475}(271, \cdot)\) None 0 4
2475.1.ci \(\chi_{2475}(226, \cdot)\) None 0 4
2475.1.ck \(\chi_{2475}(541, \cdot)\) None 0 4
2475.1.cl \(\chi_{2475}(386, \cdot)\) None 0 4
2475.1.cn \(\chi_{2475}(244, \cdot)\) None 0 4
2475.1.cp \(\chi_{2475}(944, \cdot)\) None 0 4
2475.1.cr \(\chi_{2475}(32, \cdot)\) 2475.1.cr.a 4 4
2475.1.cr.b 4
2475.1.cs \(\chi_{2475}(232, \cdot)\) None 0 4
2475.1.db \(\chi_{2475}(233, \cdot)\) None 0 8
2475.1.dc \(\chi_{2475}(388, \cdot)\) None 0 8
2475.1.df \(\chi_{2475}(163, \cdot)\) None 0 8
2475.1.dg \(\chi_{2475}(98, \cdot)\) None 0 8
2475.1.dh \(\chi_{2475}(107, \cdot)\) None 0 8
2475.1.di \(\chi_{2475}(17, \cdot)\) None 0 8
2475.1.dj \(\chi_{2475}(8, \cdot)\) None 0 8
2475.1.ds \(\chi_{2475}(82, \cdot)\) None 0 8
2475.1.dt \(\chi_{2475}(37, \cdot)\) None 0 8
2475.1.du \(\chi_{2475}(883, \cdot)\) None 0 8
2475.1.dv \(\chi_{2475}(298, \cdot)\) None 0 8
2475.1.dw \(\chi_{2475}(458, \cdot)\) None 0 8
2475.1.dz \(\chi_{2475}(104, \cdot)\) None 0 8
2475.1.ea \(\chi_{2475}(139, \cdot)\) None 0 8
2475.1.eb \(\chi_{2475}(56, \cdot)\) None 0 8
2475.1.ee \(\chi_{2475}(61, \cdot)\) None 0 8
2475.1.eh \(\chi_{2475}(151, \cdot)\) None 0 8
2475.1.ei \(\chi_{2475}(211, \cdot)\) None 0 8
2475.1.ek \(\chi_{2475}(556, \cdot)\) None 0 8
2475.1.el \(\chi_{2475}(191, \cdot)\) None 0 8
2475.1.en \(\chi_{2475}(86, \cdot)\) None 0 8
2475.1.eo \(\chi_{2475}(401, \cdot)\) None 0 8
2475.1.er \(\chi_{2475}(146, \cdot)\) None 0 8
2475.1.eu \(\chi_{2475}(241, \cdot)\) 2475.1.eu.a 8 8
2475.1.eu.b 8
2475.1.ev \(\chi_{2475}(439, \cdot)\) 2475.1.ev.a 8 8
2475.1.ev.b 8
2475.1.ew \(\chi_{2475}(599, \cdot)\) None 0 8
2475.1.ex \(\chi_{2475}(344, \cdot)\) None 0 8
2475.1.fa \(\chi_{2475}(284, \cdot)\) None 0 8
2475.1.fc \(\chi_{2475}(14, \cdot)\) None 0 8
2475.1.fe \(\chi_{2475}(79, \cdot)\) None 0 8
2475.1.ff \(\chi_{2475}(409, \cdot)\) None 0 8
2475.1.fg \(\chi_{2475}(259, \cdot)\) None 0 8
2475.1.fh \(\chi_{2475}(349, \cdot)\) None 0 8
2475.1.fi \(\chi_{2475}(254, \cdot)\) None 0 8
2475.1.fk \(\chi_{2475}(436, \cdot)\) None 0 8
2475.1.fn \(\chi_{2475}(581, \cdot)\) None 0 8
2475.1.fo \(\chi_{2475}(248, \cdot)\) None 0 16
2475.1.fu \(\chi_{2475}(58, \cdot)\) None 0 16
2475.1.fv \(\chi_{2475}(97, \cdot)\) None 0 16
2475.1.fw \(\chi_{2475}(157, \cdot)\) None 0 16
2475.1.fx \(\chi_{2475}(67, \cdot)\) None 0 16
2475.1.fy \(\chi_{2475}(263, \cdot)\) 2475.1.fy.a 16 16
2475.1.fy.b 16
2475.1.fz \(\chi_{2475}(2, \cdot)\) None 0 16
2475.1.ga \(\chi_{2475}(83, \cdot)\) None 0 16
2475.1.gb \(\chi_{2475}(68, \cdot)\) None 0 16
2475.1.gh \(\chi_{2475}(148, \cdot)\) None 0 16
2475.1.gi \(\chi_{2475}(202, \cdot)\) None 0 16
2475.1.gl \(\chi_{2475}(167, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2475))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2475)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(825))\)\(^{\oplus 2}\)