# Properties

 Label 2523.1 Level 2523 Weight 1 Dimension 82 Nonzero newspaces 4 Newform subspaces 10 Sturm bound 470960 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$2523 = 3 \cdot 29^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$10$$ Sturm bound: $$470960$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2523))$$.

Total New Old
Modular forms 2494 1231 1263
Cusp forms 86 82 4
Eisenstein series 2408 1149 1259

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 82 0 0 0

## Trace form

 $$82 q + 2 q^{6} + 2 q^{7} - 2 q^{9} + O(q^{10})$$ $$82 q + 2 q^{6} + 2 q^{7} - 2 q^{9} + 2 q^{13} + 2 q^{16} - 2 q^{22} - 2 q^{24} - 2 q^{25} + 2 q^{33} - 2 q^{34} - 2 q^{42} + 2 q^{51} + 2 q^{54} + 2 q^{63} - 2 q^{64} + 2 q^{67} - 2 q^{78} - 2 q^{81} + 4 q^{82} - 26 q^{88} - 2 q^{91} - 2 q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2523))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2523.1.b $$\chi_{2523}(842, \cdot)$$ 2523.1.b.a 2 1
2523.1.b.b 2
2523.1.b.c 2
2523.1.d $$\chi_{2523}(2522, \cdot)$$ 2523.1.d.a 4 1
2523.1.e $$\chi_{2523}(1723, \cdot)$$ None 0 2
2523.1.h $$\chi_{2523}(236, \cdot)$$ 2523.1.h.a 6 6
2523.1.h.b 6
2523.1.h.c 24
2523.1.j $$\chi_{2523}(605, \cdot)$$ 2523.1.j.a 12 6
2523.1.j.b 12
2523.1.j.c 12
2523.1.l $$\chi_{2523}(781, \cdot)$$ None 0 12
2523.1.n $$\chi_{2523}(86, \cdot)$$ None 0 28
2523.1.p $$\chi_{2523}(59, \cdot)$$ None 0 28
2523.1.r $$\chi_{2523}(46, \cdot)$$ None 0 56
2523.1.t $$\chi_{2523}(20, \cdot)$$ None 0 168
2523.1.v $$\chi_{2523}(5, \cdot)$$ None 0 168
2523.1.w $$\chi_{2523}(10, \cdot)$$ None 0 336

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(2523))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(2523)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(841))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(2523))$$$$^{\oplus 1}$$