# Properties

 Label 1521.1 Level 1521 Weight 1 Dimension 46 Nonzero newspaces 3 Newform subspaces 8 Sturm bound 170352 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$1521 = 3^{2} \cdot 13^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$8$$ Sturm bound: $$170352$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1521))$$.

Total New Old
Modular forms 1936 966 970
Cusp forms 112 46 66
Eisenstein series 1824 920 904

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 46 0 0 0

## Trace form

 $$46 q + 4 q^{7} + O(q^{10})$$ $$46 q + 4 q^{7} + 4 q^{16} + 4 q^{19} - 4 q^{28} - 4 q^{31} - 4 q^{37} - 2 q^{52} + 4 q^{67} + 4 q^{73} + 4 q^{76} + 2 q^{91} - 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1521))$$

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
1521.1.c $$\chi_{1521}(170, \cdot)$$ None 0 1
1521.1.d $$\chi_{1521}(1520, \cdot)$$ None 0 1
1521.1.j $$\chi_{1521}(577, \cdot)$$ 1521.1.j.a 2 2
1521.1.j.b 2
1521.1.j.c 2
1521.1.k $$\chi_{1521}(146, \cdot)$$ None 0 2
1521.1.m $$\chi_{1521}(23, \cdot)$$ None 0 2
1521.1.n $$\chi_{1521}(506, \cdot)$$ None 0 2
1521.1.o $$\chi_{1521}(485, \cdot)$$ None 0 2
1521.1.p $$\chi_{1521}(1160, \cdot)$$ None 0 2
1521.1.s $$\chi_{1521}(677, \cdot)$$ None 0 2
1521.1.u $$\chi_{1521}(191, \cdot)$$ None 0 2
1521.1.v $$\chi_{1521}(1037, \cdot)$$ None 0 2
1521.1.w $$\chi_{1521}(319, \cdot)$$ None 0 4
1521.1.y $$\chi_{1521}(70, \cdot)$$ None 0 4
1521.1.bb $$\chi_{1521}(418, \cdot)$$ None 0 4
1521.1.bd $$\chi_{1521}(19, \cdot)$$ 1521.1.bd.a 4 4
1521.1.bd.b 4
1521.1.bd.c 4
1521.1.bd.d 4
1521.1.bf $$\chi_{1521}(116, \cdot)$$ None 0 12
1521.1.bg $$\chi_{1521}(53, \cdot)$$ None 0 12
1521.1.bm $$\chi_{1521}(73, \cdot)$$ 1521.1.bm.a 24 24
1521.1.bo $$\chi_{1521}(95, \cdot)$$ None 0 24
1521.1.bp $$\chi_{1521}(68, \cdot)$$ None 0 24
1521.1.br $$\chi_{1521}(14, \cdot)$$ None 0 24
1521.1.bu $$\chi_{1521}(35, \cdot)$$ None 0 24
1521.1.bv $$\chi_{1521}(17, \cdot)$$ None 0 24
1521.1.bw $$\chi_{1521}(38, \cdot)$$ None 0 24
1521.1.bx $$\chi_{1521}(56, \cdot)$$ None 0 24
1521.1.bz $$\chi_{1521}(29, \cdot)$$ None 0 24
1521.1.ca $$\chi_{1521}(28, \cdot)$$ None 0 48
1521.1.cc $$\chi_{1521}(7, \cdot)$$ None 0 48
1521.1.cf $$\chi_{1521}(31, \cdot)$$ None 0 48
1521.1.ch $$\chi_{1521}(58, \cdot)$$ None 0 48

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1521))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1521)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(507))$$$$^{\oplus 2}$$