# Properties

 Label 775.1 Level 775 Weight 1 Dimension 30 Nonzero newspaces 4 Newform subspaces 8 Sturm bound 48000 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$775 = 5^{2} \cdot 31$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$8$$ Sturm bound: $$48000$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(775))$$.

Total New Old
Modular forms 879 625 254
Cusp forms 39 30 9
Eisenstein series 840 595 245

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 30 0 0 0

## Trace form

 $$30 q + q^{2} + 3 q^{4} + q^{7} - 7 q^{8} + 2 q^{9} + O(q^{10})$$ $$30 q + q^{2} + 3 q^{4} + q^{7} - 7 q^{8} + 2 q^{9} - 19 q^{14} - 6 q^{16} + q^{18} + q^{19} - 6 q^{28} - 6 q^{32} - 6 q^{35} - 3 q^{36} + 23 q^{38} - 6 q^{40} - 3 q^{41} - 8 q^{47} + 3 q^{49} - 9 q^{56} + q^{59} + q^{62} + q^{63} + 14 q^{64} - 8 q^{67} - 6 q^{70} - 3 q^{71} - 7 q^{72} - 6 q^{76} - 6 q^{80} - 7 q^{82} + 24 q^{90} + 2 q^{94} - 6 q^{95} + q^{97} - 6 q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(775))$$

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
775.1.c $$\chi_{775}(774, \cdot)$$ 775.1.c.a 2 1
775.1.d $$\chi_{775}(526, \cdot)$$ 775.1.d.a 1 1
775.1.d.b 1
775.1.d.c 2
775.1.g $$\chi_{775}(32, \cdot)$$ None 0 2
775.1.n $$\chi_{775}(99, \cdot)$$ None 0 2
775.1.p $$\chi_{775}(26, \cdot)$$ None 0 2
775.1.q $$\chi_{775}(339, \cdot)$$ None 0 4
775.1.s $$\chi_{775}(246, \cdot)$$ None 0 4
775.1.t $$\chi_{775}(151, \cdot)$$ None 0 4
775.1.u $$\chi_{775}(91, \cdot)$$ None 0 4
775.1.v $$\chi_{775}(46, \cdot)$$ None 0 4
775.1.w $$\chi_{775}(61, \cdot)$$ 775.1.w.a 4 4
775.1.w.b 8
775.1.y $$\chi_{775}(399, \cdot)$$ None 0 4
775.1.z $$\chi_{775}(154, \cdot)$$ 775.1.z.a 4 4
775.1.z.b 8
775.1.ba $$\chi_{775}(89, \cdot)$$ None 0 4
775.1.bb $$\chi_{775}(54, \cdot)$$ None 0 4
775.1.bg $$\chi_{775}(29, \cdot)$$ None 0 4
775.1.bh $$\chi_{775}(581, \cdot)$$ None 0 4
775.1.bi $$\chi_{775}(118, \cdot)$$ None 0 4
775.1.bq $$\chi_{775}(2, \cdot)$$ None 0 8
775.1.bt $$\chi_{775}(233, \cdot)$$ None 0 8
775.1.bu $$\chi_{775}(33, \cdot)$$ None 0 8
775.1.bv $$\chi_{775}(63, \cdot)$$ None 0 8
775.1.bw $$\chi_{775}(188, \cdot)$$ None 0 8
775.1.cb $$\chi_{775}(132, \cdot)$$ None 0 8
775.1.cd $$\chi_{775}(34, \cdot)$$ None 0 8
775.1.ce $$\chi_{775}(6, \cdot)$$ None 0 8
775.1.cf $$\chi_{775}(11, \cdot)$$ None 0 8
775.1.cg $$\chi_{775}(146, \cdot)$$ None 0 8
775.1.ch $$\chi_{775}(176, \cdot)$$ None 0 8
775.1.ci $$\chi_{775}(21, \cdot)$$ None 0 8
775.1.cj $$\chi_{775}(44, \cdot)$$ None 0 8
775.1.co $$\chi_{775}(79, \cdot)$$ None 0 8
775.1.cp $$\chi_{775}(84, \cdot)$$ None 0 8
775.1.cq $$\chi_{775}(119, \cdot)$$ None 0 8
775.1.cr $$\chi_{775}(24, \cdot)$$ None 0 8
775.1.ct $$\chi_{775}(136, \cdot)$$ None 0 8
775.1.cv $$\chi_{775}(133, \cdot)$$ None 0 16
775.1.cw $$\chi_{775}(7, \cdot)$$ None 0 16
775.1.db $$\chi_{775}(112, \cdot)$$ None 0 16
775.1.dc $$\chi_{775}(67, \cdot)$$ None 0 16
775.1.dd $$\chi_{775}(28, \cdot)$$ None 0 16
775.1.de $$\chi_{775}(38, \cdot)$$ None 0 16

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(775))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(775)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(155))$$$$^{\oplus 2}$$