# Properties

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

## 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

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