# Properties

 Label 1575.1 Level 1575 Weight 1 Dimension 83 Nonzero newspaces 10 Newform subspaces 20 Sturm bound 172800 Trace bound 16

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$10$$ Newform subspaces: $$20$$ Sturm bound: $$172800$$ Trace bound: $$16$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1575))$$.

Total New Old
Modular forms 2838 1006 1832
Cusp forms 150 83 67
Eisenstein series 2688 923 1765

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 67 16 0 0

## Trace form

 $$83 q + 3 q^{4} + 8 q^{6} + q^{7} - 4 q^{9} + O(q^{10})$$ $$83 q + 3 q^{4} + 8 q^{6} + q^{7} - 4 q^{9} - 6 q^{11} - 11 q^{16} - 2 q^{21} - 8 q^{26} - q^{28} + 4 q^{29} + 4 q^{31} + 2 q^{36} + 2 q^{37} - 2 q^{39} - 8 q^{41} + 2 q^{43} + 4 q^{44} - 20 q^{46} + q^{49} - 8 q^{51} - 8 q^{56} - 4 q^{61} - 3 q^{64} - 2 q^{67} - 32 q^{71} - 8 q^{76} - 4 q^{79} - 8 q^{81} - 4 q^{84} - 8 q^{86} + 12 q^{91} - 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1575))$$

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
1575.1.c $$\chi_{1575}(701, \cdot)$$ None 0 1
1575.1.e $$\chi_{1575}(874, \cdot)$$ 1575.1.e.a 2 1
1575.1.e.b 2
1575.1.e.c 4
1575.1.f $$\chi_{1575}(449, \cdot)$$ None 0 1
1575.1.h $$\chi_{1575}(1126, \cdot)$$ 1575.1.h.a 1 1
1575.1.h.b 1
1575.1.h.c 1
1575.1.h.d 2
1575.1.h.e 2
1575.1.n $$\chi_{1575}(818, \cdot)$$ 1575.1.n.a 4 2
1575.1.n.b 4
1575.1.n.c 8
1575.1.n.d 8
1575.1.o $$\chi_{1575}(568, \cdot)$$ None 0 2
1575.1.r $$\chi_{1575}(1174, \cdot)$$ None 0 2
1575.1.t $$\chi_{1575}(326, \cdot)$$ None 0 2
1575.1.w $$\chi_{1575}(599, \cdot)$$ None 0 2
1575.1.x $$\chi_{1575}(451, \cdot)$$ 1575.1.x.a 2 2
1575.1.x.b 2
1575.1.y $$\chi_{1575}(76, \cdot)$$ 1575.1.y.a 4 2
1575.1.z $$\chi_{1575}(674, \cdot)$$ None 0 2
1575.1.bb $$\chi_{1575}(974, \cdot)$$ None 0 2
1575.1.bd $$\chi_{1575}(376, \cdot)$$ None 0 2
1575.1.be $$\chi_{1575}(851, \cdot)$$ None 0 2
1575.1.bh $$\chi_{1575}(349, \cdot)$$ None 0 2
1575.1.bj $$\chi_{1575}(199, \cdot)$$ 1575.1.bj.a 4 2
1575.1.bl $$\chi_{1575}(176, \cdot)$$ None 0 2
1575.1.bn $$\chi_{1575}(926, \cdot)$$ None 0 2
1575.1.bo $$\chi_{1575}(124, \cdot)$$ None 0 2
1575.1.bq $$\chi_{1575}(1426, \cdot)$$ None 0 2
1575.1.bs $$\chi_{1575}(74, \cdot)$$ None 0 2
1575.1.bt $$\chi_{1575}(181, \cdot)$$ None 0 4
1575.1.bv $$\chi_{1575}(134, \cdot)$$ None 0 4
1575.1.bw $$\chi_{1575}(244, \cdot)$$ None 0 4
1575.1.by $$\chi_{1575}(71, \cdot)$$ None 0 4
1575.1.cb $$\chi_{1575}(718, \cdot)$$ 1575.1.cb.a 8 4
1575.1.cc $$\chi_{1575}(68, \cdot)$$ None 0 4
1575.1.ce $$\chi_{1575}(1118, \cdot)$$ None 0 4
1575.1.cg $$\chi_{1575}(43, \cdot)$$ None 0 4
1575.1.ci $$\chi_{1575}(793, \cdot)$$ 1575.1.ci.a 8 4
1575.1.cl $$\chi_{1575}(143, \cdot)$$ None 0 4
1575.1.cn $$\chi_{1575}(293, \cdot)$$ 1575.1.cn.a 8 4
1575.1.cp $$\chi_{1575}(193, \cdot)$$ 1575.1.cp.a 8 4
1575.1.cv $$\chi_{1575}(127, \cdot)$$ None 0 8
1575.1.cw $$\chi_{1575}(62, \cdot)$$ None 0 8
1575.1.cy $$\chi_{1575}(389, \cdot)$$ None 0 8
1575.1.da $$\chi_{1575}(166, \cdot)$$ None 0 8
1575.1.dc $$\chi_{1575}(94, \cdot)$$ None 0 8
1575.1.dd $$\chi_{1575}(116, \cdot)$$ None 0 8
1575.1.df $$\chi_{1575}(281, \cdot)$$ None 0 8
1575.1.dh $$\chi_{1575}(19, \cdot)$$ None 0 8
1575.1.dj $$\chi_{1575}(34, \cdot)$$ None 0 8
1575.1.dm $$\chi_{1575}(191, \cdot)$$ None 0 8
1575.1.dn $$\chi_{1575}(31, \cdot)$$ None 0 8
1575.1.dp $$\chi_{1575}(29, \cdot)$$ None 0 8
1575.1.dr $$\chi_{1575}(44, \cdot)$$ None 0 8
1575.1.ds $$\chi_{1575}(286, \cdot)$$ None 0 8
1575.1.dt $$\chi_{1575}(136, \cdot)$$ None 0 8
1575.1.du $$\chi_{1575}(254, \cdot)$$ None 0 8
1575.1.dx $$\chi_{1575}(11, \cdot)$$ None 0 8
1575.1.dz $$\chi_{1575}(229, \cdot)$$ None 0 8
1575.1.ea $$\chi_{1575}(67, \cdot)$$ None 0 16
1575.1.ec $$\chi_{1575}(83, \cdot)$$ None 0 16
1575.1.ee $$\chi_{1575}(17, \cdot)$$ None 0 16
1575.1.eh $$\chi_{1575}(37, \cdot)$$ None 0 16
1575.1.ej $$\chi_{1575}(22, \cdot)$$ None 0 16
1575.1.el $$\chi_{1575}(47, \cdot)$$ None 0 16
1575.1.en $$\chi_{1575}(38, \cdot)$$ None 0 16
1575.1.eo $$\chi_{1575}(58, \cdot)$$ None 0 16

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1575))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1575)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(315))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(525))$$$$^{\oplus 2}$$