# Properties

 Label 1775.1 Level 1775 Weight 1 Dimension 72 Nonzero newspaces 4 Newform subspaces 8 Sturm bound 252000 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$1775 = 5^{2} \cdot 71$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$8$$ Sturm bound: $$252000$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1775))$$.

Total New Old
Modular forms 2055 1487 568
Cusp forms 95 72 23
Eisenstein series 1960 1415 545

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 72 0 0 0

## Trace form

 $$72 q + q^{2} + q^{3} + 5 q^{4} - 6 q^{6} + 2 q^{8} + 5 q^{9} + O(q^{10})$$ $$72 q + q^{2} + q^{3} + 5 q^{4} - 6 q^{6} + 2 q^{8} + 5 q^{9} + 3 q^{12} - 4 q^{16} - 18 q^{18} + q^{19} - 45 q^{24} + 2 q^{27} + q^{29} + 3 q^{32} - 10 q^{36} + q^{37} - 19 q^{38} + q^{43} - 16 q^{48} + 4 q^{49} + 4 q^{54} + 2 q^{57} + 2 q^{58} + 7 q^{64} + 2 q^{71} + 55 q^{72} + q^{73} - 47 q^{74} - 14 q^{75} - 9 q^{76} + q^{79} + 56 q^{80} - 4 q^{81} + q^{83} - 6 q^{86} - 19 q^{87} + q^{89} - 11 q^{96} + q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1775))$$

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
1775.1.c $$\chi_{1775}(1774, \cdot)$$ 1775.1.c.a 6 1
1775.1.d $$\chi_{1775}(851, \cdot)$$ 1775.1.d.a 1 1
1775.1.d.b 3
1775.1.d.c 6
1775.1.f $$\chi_{1775}(143, \cdot)$$ None 0 2
1775.1.n $$\chi_{1775}(259, \cdot)$$ None 0 4
1775.1.p $$\chi_{1775}(141, \cdot)$$ 1775.1.p.a 4 4
1775.1.p.b 24
1775.1.q $$\chi_{1775}(301, \cdot)$$ None 0 4
1775.1.r $$\chi_{1775}(66, \cdot)$$ None 0 4
1775.1.s $$\chi_{1775}(1111, \cdot)$$ None 0 4
1775.1.t $$\chi_{1775}(46, \cdot)$$ None 0 4
1775.1.u $$\chi_{1775}(869, \cdot)$$ None 0 4
1775.1.x $$\chi_{1775}(14, \cdot)$$ None 0 4
1775.1.y $$\chi_{1775}(724, \cdot)$$ None 0 4
1775.1.bb $$\chi_{1775}(354, \cdot)$$ 1775.1.bb.a 4 4
1775.1.bb.b 24
1775.1.bc $$\chi_{1775}(159, \cdot)$$ None 0 4
1775.1.be $$\chi_{1775}(156, \cdot)$$ None 0 4
1775.1.bf $$\chi_{1775}(26, \cdot)$$ None 0 6
1775.1.bg $$\chi_{1775}(449, \cdot)$$ None 0 6
1775.1.bj $$\chi_{1775}(147, \cdot)$$ None 0 8
1775.1.bk $$\chi_{1775}(267, \cdot)$$ None 0 8
1775.1.bm $$\chi_{1775}(167, \cdot)$$ None 0 8
1775.1.bn $$\chi_{1775}(72, \cdot)$$ None 0 8
1775.1.bo $$\chi_{1775}(57, \cdot)$$ None 0 8
1775.1.bs $$\chi_{1775}(128, \cdot)$$ None 0 8
1775.1.bu $$\chi_{1775}(32, \cdot)$$ None 0 12
1775.1.cc $$\chi_{1775}(61, \cdot)$$ None 0 24
1775.1.ce $$\chi_{1775}(44, \cdot)$$ None 0 24
1775.1.cf $$\chi_{1775}(34, \cdot)$$ None 0 24
1775.1.ci $$\chi_{1775}(99, \cdot)$$ None 0 24
1775.1.cj $$\chi_{1775}(59, \cdot)$$ None 0 24
1775.1.cm $$\chi_{1775}(209, \cdot)$$ None 0 24
1775.1.cn $$\chi_{1775}(56, \cdot)$$ None 0 24
1775.1.co $$\chi_{1775}(11, \cdot)$$ None 0 24
1775.1.cp $$\chi_{1775}(31, \cdot)$$ None 0 24
1775.1.cq $$\chi_{1775}(126, \cdot)$$ None 0 24
1775.1.cr $$\chi_{1775}(41, \cdot)$$ None 0 24
1775.1.ct $$\chi_{1775}(189, \cdot)$$ None 0 24
1775.1.cv $$\chi_{1775}(2, \cdot)$$ None 0 48
1775.1.cz $$\chi_{1775}(12, \cdot)$$ None 0 48
1775.1.da $$\chi_{1775}(18, \cdot)$$ None 0 48
1775.1.db $$\chi_{1775}(37, \cdot)$$ None 0 48
1775.1.dd $$\chi_{1775}(3, \cdot)$$ None 0 48
1775.1.de $$\chi_{1775}(152, \cdot)$$ None 0 48

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1775))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1775)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(71))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(355))$$$$^{\oplus 2}$$