## Defining parameters

 Level: $$N$$ = $$2151 = 3^{2} \cdot 239$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$7$$ Sturm bound: $$342720$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2151))$$.

Total New Old
Modular forms 1966 1108 858
Cusp forms 62 41 21
Eisenstein series 1904 1067 837

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 37 0 4 0

## Trace form

 $$41q + q^{2} - 9q^{4} + q^{5} + 2q^{8} + O(q^{10})$$ $$41q + q^{2} - 9q^{4} + q^{5} + 2q^{8} - 6q^{10} + q^{11} - 14q^{16} + q^{17} + 3q^{20} - 6q^{22} - 9q^{25} + q^{29} - 5q^{31} + 3q^{32} - 6q^{34} + 3q^{44} - 12q^{49} + 3q^{50} + 2q^{55} - 6q^{58} - 15q^{60} + 3q^{61} - 43q^{62} + 38q^{64} + 30q^{66} - 5q^{67} + 3q^{68} + q^{71} - 15q^{72} + 50q^{80} + q^{83} + 2q^{85} - 15q^{90} + 8q^{91} + q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2151))$$

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
2151.1.c $$\chi_{2151}(1196, \cdot)$$ None 0 1
2151.1.d $$\chi_{2151}(955, \cdot)$$ 2151.1.d.a 1 1
2151.1.d.b 2
2151.1.d.c 2
2151.1.d.d 2
2151.1.d.e 4
2151.1.f $$\chi_{2151}(238, \cdot)$$ 2151.1.f.a 6 2
2151.1.f.b 24
2151.1.g $$\chi_{2151}(479, \cdot)$$ None 0 2
2151.1.j $$\chi_{2151}(856, \cdot)$$ None 0 6
2151.1.k $$\chi_{2151}(44, \cdot)$$ None 0 6
2151.1.o $$\chi_{2151}(28, \cdot)$$ None 0 16
2151.1.p $$\chi_{2151}(71, \cdot)$$ None 0 16
2151.1.s $$\chi_{2151}(263, \cdot)$$ None 0 12
2151.1.t $$\chi_{2151}(139, \cdot)$$ None 0 12
2151.1.w $$\chi_{2151}(101, \cdot)$$ None 0 32
2151.1.x $$\chi_{2151}(52, \cdot)$$ None 0 32
2151.1.ba $$\chi_{2151}(8, \cdot)$$ None 0 96
2151.1.bb $$\chi_{2151}(19, \cdot)$$ None 0 96
2151.1.bd $$\chi_{2151}(7, \cdot)$$ None 0 192
2151.1.be $$\chi_{2151}(2, \cdot)$$ None 0 192

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(2151))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(2151)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(239))$$$$^{\oplus 3}$$