# Properties

 Label 1020.1 Level 1020 Weight 1 Dimension 36 Nonzero newspaces 2 Newform subspaces 3 Sturm bound 55296 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$3$$ Sturm bound: $$55296$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1020))$$.

Total New Old
Modular forms 1434 212 1222
Cusp forms 154 36 118
Eisenstein series 1280 176 1104

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 36 0 0 0

## Trace form

 $$36q - 4q^{9} + O(q^{10})$$ $$36q - 4q^{9} + 2q^{15} - 4q^{19} - 16q^{24} + 2q^{25} - 16q^{34} - 16q^{36} - 16q^{46} - 4q^{49} - 4q^{51} + 6q^{55} - 4q^{69} + 4q^{81} + 2q^{85} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1020))$$

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
1020.1.c $$\chi_{1020}(749, \cdot)$$ None 0 1
1020.1.d $$\chi_{1020}(511, \cdot)$$ None 0 1
1020.1.f $$\chi_{1020}(679, \cdot)$$ None 0 1
1020.1.i $$\chi_{1020}(101, \cdot)$$ None 0 1
1020.1.j $$\chi_{1020}(919, \cdot)$$ None 0 1
1020.1.m $$\chi_{1020}(341, \cdot)$$ None 0 1
1020.1.o $$\chi_{1020}(509, \cdot)$$ 1020.1.o.a 4 1
1020.1.p $$\chi_{1020}(271, \cdot)$$ None 0 1
1020.1.q $$\chi_{1020}(47, \cdot)$$ None 0 2
1020.1.t $$\chi_{1020}(13, \cdot)$$ None 0 2
1020.1.u $$\chi_{1020}(373, \cdot)$$ None 0 2
1020.1.x $$\chi_{1020}(203, \cdot)$$ None 0 2
1020.1.z $$\chi_{1020}(89, \cdot)$$ None 0 2
1020.1.bb $$\chi_{1020}(259, \cdot)$$ None 0 2
1020.1.bc $$\chi_{1020}(701, \cdot)$$ None 0 2
1020.1.be $$\chi_{1020}(871, \cdot)$$ None 0 2
1020.1.bh $$\chi_{1020}(613, \cdot)$$ None 0 2
1020.1.bi $$\chi_{1020}(443, \cdot)$$ None 0 2
1020.1.bl $$\chi_{1020}(863, \cdot)$$ None 0 2
1020.1.bm $$\chi_{1020}(217, \cdot)$$ None 0 2
1020.1.bq $$\chi_{1020}(151, \cdot)$$ None 0 4
1020.1.br $$\chi_{1020}(161, \cdot)$$ None 0 4
1020.1.bu $$\chi_{1020}(83, \cdot)$$ None 0 4
1020.1.bv $$\chi_{1020}(433, \cdot)$$ None 0 4
1020.1.bw $$\chi_{1020}(253, \cdot)$$ None 0 4
1020.1.bx $$\chi_{1020}(263, \cdot)$$ None 0 4
1020.1.ca $$\chi_{1020}(389, \cdot)$$ None 0 4
1020.1.cb $$\chi_{1020}(19, \cdot)$$ None 0 4
1020.1.ce $$\chi_{1020}(7, \cdot)$$ None 0 8
1020.1.cf $$\chi_{1020}(173, \cdot)$$ None 0 8
1020.1.cj $$\chi_{1020}(61, \cdot)$$ None 0 8
1020.1.cl $$\chi_{1020}(299, \cdot)$$ 1020.1.cl.a 16 8
1020.1.cl.b 16
1020.1.cm $$\chi_{1020}(109, \cdot)$$ None 0 8
1020.1.co $$\chi_{1020}(11, \cdot)$$ None 0 8
1020.1.cs $$\chi_{1020}(163, \cdot)$$ None 0 8
1020.1.ct $$\chi_{1020}(113, \cdot)$$ None 0 8

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1020))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1020)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(204))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(255))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(340))$$$$^{\oplus 2}$$