# Properties

 Label 1045.1 Level 1045 Weight 1 Dimension 64 Nonzero newspaces 3 Newform subspaces 12 Sturm bound 86400 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$1045 = 5 \cdot 11 \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$12$$ Sturm bound: $$86400$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1045))$$.

Total New Old
Modular forms 1528 984 544
Cusp forms 88 64 24
Eisenstein series 1440 920 520

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 64 0 0 0

## Trace form

 $$64 q - 6 q^{4} - 2 q^{5} - 10 q^{7} - 6 q^{9} + O(q^{10})$$ $$64 q - 6 q^{4} - 2 q^{5} - 10 q^{7} - 6 q^{9} + 6 q^{11} - 6 q^{16} - 10 q^{17} - 2 q^{19} + 6 q^{20} - 4 q^{23} - 16 q^{24} - 14 q^{25} - 24 q^{26} - 16 q^{30} - 5 q^{35} + 18 q^{36} + 4 q^{38} - 2 q^{45} - 4 q^{47} + 64 q^{54} - 3 q^{55} - 8 q^{58} - 6 q^{61} + 10 q^{63} - 6 q^{64} - 8 q^{66} + 10 q^{68} - 8 q^{76} + 17 q^{80} - 14 q^{81} - 5 q^{85} - 4 q^{92} - 15 q^{95} + 8 q^{96} - 10 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1045))$$

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
1045.1.c $$\chi_{1045}(56, \cdot)$$ None 0 1
1045.1.d $$\chi_{1045}(571, \cdot)$$ None 0 1
1045.1.g $$\chi_{1045}(989, \cdot)$$ None 0 1
1045.1.h $$\chi_{1045}(474, \cdot)$$ None 0 1
1045.1.k $$\chi_{1045}(208, \cdot)$$ 1045.1.k.a 2 2
1045.1.k.b 2
1045.1.k.c 2
1045.1.k.d 2
1045.1.l $$\chi_{1045}(628, \cdot)$$ None 0 2
1045.1.o $$\chi_{1045}(639, \cdot)$$ None 0 2
1045.1.q $$\chi_{1045}(714, \cdot)$$ None 0 2
1045.1.r $$\chi_{1045}(296, \cdot)$$ None 0 2
1045.1.u $$\chi_{1045}(221, \cdot)$$ None 0 2
1045.1.w $$\chi_{1045}(284, \cdot)$$ 1045.1.w.a 4 4
1045.1.w.b 4
1045.1.w.c 4
1045.1.w.d 4
1045.1.w.e 8
1045.1.w.f 16
1045.1.x $$\chi_{1045}(39, \cdot)$$ None 0 4
1045.1.ba $$\chi_{1045}(96, \cdot)$$ None 0 4
1045.1.bb $$\chi_{1045}(246, \cdot)$$ None 0 4
1045.1.be $$\chi_{1045}(353, \cdot)$$ None 0 4
1045.1.bf $$\chi_{1045}(373, \cdot)$$ None 0 4
1045.1.bi $$\chi_{1045}(54, \cdot)$$ None 0 6
1045.1.bk $$\chi_{1045}(166, \cdot)$$ None 0 6
1045.1.bl $$\chi_{1045}(34, \cdot)$$ None 0 6
1045.1.bn $$\chi_{1045}(131, \cdot)$$ None 0 6
1045.1.bq $$\chi_{1045}(58, \cdot)$$ None 0 8
1045.1.br $$\chi_{1045}(18, \cdot)$$ 1045.1.br.a 8 8
1045.1.br.b 8
1045.1.bt $$\chi_{1045}(31, \cdot)$$ None 0 8
1045.1.bw $$\chi_{1045}(106, \cdot)$$ None 0 8
1045.1.bx $$\chi_{1045}(239, \cdot)$$ None 0 8
1045.1.bz $$\chi_{1045}(69, \cdot)$$ None 0 8
1045.1.ca $$\chi_{1045}(23, \cdot)$$ None 0 12
1045.1.cd $$\chi_{1045}(32, \cdot)$$ None 0 12
1045.1.cg $$\chi_{1045}(8, \cdot)$$ None 0 16
1045.1.ch $$\chi_{1045}(102, \cdot)$$ None 0 16
1045.1.cj $$\chi_{1045}(6, \cdot)$$ None 0 24
1045.1.cl $$\chi_{1045}(14, \cdot)$$ None 0 24
1045.1.co $$\chi_{1045}(71, \cdot)$$ None 0 24
1045.1.cp $$\chi_{1045}(24, \cdot)$$ None 0 24
1045.1.cq $$\chi_{1045}(2, \cdot)$$ None 0 48
1045.1.ct $$\chi_{1045}(42, \cdot)$$ None 0 48

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1045))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1045)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(209))$$$$^{\oplus 2}$$