# Properties

 Label 2775.1 Level 2775 Weight 1 Dimension 213 Nonzero newspaces 18 Newform subspaces 27 Sturm bound 547200 Trace bound 64

## Defining parameters

 Level: $$N$$ = $$2775 = 3 \cdot 5^{2} \cdot 37$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$18$$ Newform subspaces: $$27$$ Sturm bound: $$547200$$ Trace bound: $$64$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2775))$$.

Total New Old
Modular forms 4282 1647 2635
Cusp forms 250 213 37
Eisenstein series 4032 1434 2598

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 213 0 0 0

## Trace form

 $$213q + 3q^{3} + 7q^{4} + 2q^{7} + 7q^{9} + O(q^{10})$$ $$213q + 3q^{3} + 7q^{4} + 2q^{7} + 7q^{9} + 3q^{12} + 2q^{13} - 17q^{16} + 2q^{19} - 6q^{21} - 3q^{27} - 20q^{28} - 6q^{31} - 52q^{34} - 5q^{36} - 3q^{37} - 4q^{39} + 2q^{43} - 12q^{46} - 23q^{48} + 7q^{49} + 2q^{52} + 2q^{57} - 20q^{58} - 6q^{61} + 2q^{63} + 11q^{64} + 2q^{67} + 2q^{73} - 6q^{76} + 2q^{79} - 5q^{81} + 34q^{84} - 18q^{91} + 2q^{93} + 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2775))$$

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
2775.1.b $$\chi_{2775}(2774, \cdot)$$ 2775.1.b.a 2 1
2775.1.b.b 4
2775.1.d $$\chi_{2775}(926, \cdot)$$ None 0 1
2775.1.f $$\chi_{2775}(149, \cdot)$$ None 0 1
2775.1.h $$\chi_{2775}(776, \cdot)$$ 2775.1.h.a 1 1
2775.1.h.b 2
2775.1.h.c 4
2775.1.h.d 4
2775.1.k $$\chi_{2775}(68, \cdot)$$ 2775.1.k.a 4 2
2775.1.l $$\chi_{2775}(1474, \cdot)$$ None 0 2
2775.1.p $$\chi_{2775}(2332, \cdot)$$ None 0 2
2775.1.q $$\chi_{2775}(2182, \cdot)$$ None 0 2
2775.1.r $$\chi_{2775}(376, \cdot)$$ None 0 2
2775.1.u $$\chi_{2775}(968, \cdot)$$ 2775.1.u.a 4 2
2775.1.w $$\chi_{2775}(101, \cdot)$$ 2775.1.w.a 2 2
2775.1.x $$\chi_{2775}(824, \cdot)$$ 2775.1.x.a 4 2
2775.1.z $$\chi_{2775}(26, \cdot)$$ 2775.1.z.a 2 2
2775.1.bb $$\chi_{2775}(899, \cdot)$$ 2775.1.bb.a 4 2
2775.1.bf $$\chi_{2775}(704, \cdot)$$ None 0 4
2775.1.bg $$\chi_{2775}(221, \cdot)$$ 2775.1.bg.a 4 4
2775.1.bg.b 4
2775.1.bg.c 8
2775.1.bg.d 16
2775.1.bi $$\chi_{2775}(554, \cdot)$$ 2775.1.bi.a 32 4
2775.1.bk $$\chi_{2775}(371, \cdot)$$ None 0 4
2775.1.bm $$\chi_{2775}(1118, \cdot)$$ 2775.1.bm.a 8 4
2775.1.bn $$\chi_{2775}(526, \cdot)$$ None 0 4
2775.1.br $$\chi_{2775}(232, \cdot)$$ None 0 4
2775.1.bs $$\chi_{2775}(307, \cdot)$$ None 0 4
2775.1.bt $$\chi_{2775}(199, \cdot)$$ None 0 4
2775.1.bw $$\chi_{2775}(1007, \cdot)$$ 2775.1.bw.a 8 4
2775.1.bz $$\chi_{2775}(176, \cdot)$$ 2775.1.bz.a 6 6
2775.1.bz.b 6
2775.1.ca $$\chi_{2775}(599, \cdot)$$ 2775.1.ca.a 12 6
2775.1.cd $$\chi_{2775}(299, \cdot)$$ 2775.1.cd.a 12 6
2775.1.ce $$\chi_{2775}(551, \cdot)$$ 2775.1.ce.a 6 6
2775.1.ce.b 6
2775.1.cf $$\chi_{2775}(413, \cdot)$$ None 0 8
2775.1.ci $$\chi_{2775}(154, \cdot)$$ None 0 8
2775.1.cj $$\chi_{2775}(73, \cdot)$$ None 0 8
2775.1.ck $$\chi_{2775}(112, \cdot)$$ None 0 8
2775.1.co $$\chi_{2775}(31, \cdot)$$ None 0 8
2775.1.cp $$\chi_{2775}(302, \cdot)$$ None 0 8
2775.1.cs $$\chi_{2775}(491, \cdot)$$ None 0 8
2775.1.cu $$\chi_{2775}(344, \cdot)$$ None 0 8
2775.1.cv $$\chi_{2775}(11, \cdot)$$ None 0 8
2775.1.cx $$\chi_{2775}(269, \cdot)$$ None 0 8
2775.1.cy $$\chi_{2775}(32, \cdot)$$ 2775.1.cy.a 24 12
2775.1.da $$\chi_{2775}(1057, \cdot)$$ None 0 12
2775.1.dd $$\chi_{2775}(7, \cdot)$$ None 0 12
2775.1.df $$\chi_{2775}(124, \cdot)$$ None 0 12
2775.1.dg $$\chi_{2775}(76, \cdot)$$ None 0 12
2775.1.di $$\chi_{2775}(143, \cdot)$$ 2775.1.di.a 24 12
2775.1.dl $$\chi_{2775}(452, \cdot)$$ None 0 16
2775.1.do $$\chi_{2775}(421, \cdot)$$ None 0 16
2775.1.dp $$\chi_{2775}(397, \cdot)$$ None 0 16
2775.1.dq $$\chi_{2775}(322, \cdot)$$ None 0 16
2775.1.du $$\chi_{2775}(214, \cdot)$$ None 0 16
2775.1.dv $$\chi_{2775}(8, \cdot)$$ None 0 16
2775.1.dx $$\chi_{2775}(71, \cdot)$$ None 0 24
2775.1.dy $$\chi_{2775}(104, \cdot)$$ None 0 24
2775.1.eb $$\chi_{2775}(44, \cdot)$$ None 0 24
2775.1.ec $$\chi_{2775}(41, \cdot)$$ None 0 24
2775.1.ef $$\chi_{2775}(17, \cdot)$$ None 0 48
2775.1.eh $$\chi_{2775}(61, \cdot)$$ None 0 48
2775.1.ei $$\chi_{2775}(19, \cdot)$$ None 0 48
2775.1.ek $$\chi_{2775}(127, \cdot)$$ None 0 48
2775.1.en $$\chi_{2775}(28, \cdot)$$ None 0 48
2775.1.ep $$\chi_{2775}(2, \cdot)$$ None 0 48

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(2775))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(2775)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(111))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(555))$$$$^{\oplus 2}$$