# Properties

 Label 1375.1 Level 1375 Weight 1 Dimension 88 Nonzero newspaces 8 Newform subspaces 13 Sturm bound 150000 Trace bound 5

# Learn more

## Defining parameters

 Level: $$N$$ = $$1375 = 5^{3} \cdot 11$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$8$$ Newform subspaces: $$13$$ Sturm bound: $$150000$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1375))$$.

Total New Old
Modular forms 1909 1240 669
Cusp forms 109 88 21
Eisenstein series 1800 1152 648

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 88 0 0 0

## Trace form

 $$88q + 2q^{3} + 4q^{9} + O(q^{10})$$ $$88q + 2q^{3} + 4q^{9} + 2q^{11} + 2q^{12} + 2q^{23} - 10q^{25} - 8q^{26} - 16q^{27} + 4q^{31} + 2q^{33} + 12q^{36} + 2q^{37} + 2q^{44} + 2q^{47} + 2q^{48} + 2q^{53} - 16q^{56} - 16q^{59} - 10q^{60} - 10q^{61} + 2q^{67} + 4q^{69} - 14q^{71} - 4q^{81} - 8q^{86} - 8q^{91} - 18q^{92} - 16q^{93} + 2q^{97} - 18q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1375))$$

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
1375.1.c $$\chi_{1375}(626, \cdot)$$ 1375.1.c.a 4 1
1375.1.c.b 4
1375.1.d $$\chi_{1375}(1374, \cdot)$$ 1375.1.d.a 2 1
1375.1.d.b 2
1375.1.d.c 4
1375.1.f $$\chi_{1375}(1057, \cdot)$$ None 0 2
1375.1.m $$\chi_{1375}(51, \cdot)$$ None 0 4
1375.1.o $$\chi_{1375}(24, \cdot)$$ None 0 4
1375.1.p $$\chi_{1375}(299, \cdot)$$ None 0 4
1375.1.q $$\chi_{1375}(249, \cdot)$$ 1375.1.q.a 4 4
1375.1.r $$\chi_{1375}(349, \cdot)$$ None 0 4
1375.1.s $$\chi_{1375}(274, \cdot)$$ 1375.1.s.a 4 4
1375.1.s.b 8
1375.1.u $$\chi_{1375}(976, \cdot)$$ None 0 4
1375.1.v $$\chi_{1375}(76, \cdot)$$ 1375.1.v.a 4 4
1375.1.v.b 8
1375.1.w $$\chi_{1375}(151, \cdot)$$ None 0 4
1375.1.x $$\chi_{1375}(376, \cdot)$$ 1375.1.x.a 4 4
1375.1.bc $$\chi_{1375}(101, \cdot)$$ None 0 4
1375.1.bd $$\chi_{1375}(149, \cdot)$$ None 0 4
1375.1.be $$\chi_{1375}(168, \cdot)$$ None 0 8
1375.1.bh $$\chi_{1375}(157, \cdot)$$ None 0 8
1375.1.bi $$\chi_{1375}(232, \cdot)$$ None 0 8
1375.1.bj $$\chi_{1375}(82, \cdot)$$ None 0 8
1375.1.bk $$\chi_{1375}(432, \cdot)$$ None 0 8
1375.1.bp $$\chi_{1375}(93, \cdot)$$ None 0 8
1375.1.bw $$\chi_{1375}(41, \cdot)$$ None 0 20
1375.1.bx $$\chi_{1375}(39, \cdot)$$ None 0 20
1375.1.by $$\chi_{1375}(19, \cdot)$$ None 0 20
1375.1.bz $$\chi_{1375}(54, \cdot)$$ 1375.1.bz.a 20 20
1375.1.ca $$\chi_{1375}(79, \cdot)$$ None 0 20
1375.1.cc $$\chi_{1375}(6, \cdot)$$ None 0 20
1375.1.cd $$\chi_{1375}(61, \cdot)$$ None 0 20
1375.1.cg $$\chi_{1375}(116, \cdot)$$ None 0 20
1375.1.ch $$\chi_{1375}(21, \cdot)$$ 1375.1.ch.a 20 20
1375.1.cj $$\chi_{1375}(139, \cdot)$$ None 0 20
1375.1.ck $$\chi_{1375}(3, \cdot)$$ None 0 40
1375.1.cp $$\chi_{1375}(42, \cdot)$$ None 0 40
1375.1.cq $$\chi_{1375}(12, \cdot)$$ None 0 40
1375.1.cr $$\chi_{1375}(38, \cdot)$$ None 0 40
1375.1.cs $$\chi_{1375}(37, \cdot)$$ None 0 40

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1375))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1375)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 2}$$