## Defining parameters

 Level: $$N$$ = $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$5$$ Newform subspaces: $$5$$ Sturm bound: $$18432$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(576))$$.

Total New Old
Modular forms 620 112 508
Cusp forms 44 13 31
Eisenstein series 576 99 477

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 9 4 0 0

## Trace form

 $$13 q - 2 q^{5} - 2 q^{9} + O(q^{10})$$ $$13 q - 2 q^{5} - 2 q^{9} + 4 q^{13} - 2 q^{21} + q^{25} + 2 q^{29} - 8 q^{33} + 2 q^{37} - 8 q^{41} + 2 q^{45} - 5 q^{49} + 2 q^{57} - 4 q^{61} + 2 q^{65} - 2 q^{69} - 10 q^{73} + 2 q^{77} + 2 q^{81} - 4 q^{85} - 2 q^{93} - 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(576))$$

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
576.1.b $$\chi_{576}(415, \cdot)$$ 576.1.b.a 2 1
576.1.e $$\chi_{576}(449, \cdot)$$ 576.1.e.a 2 1
576.1.g $$\chi_{576}(127, \cdot)$$ 576.1.g.a 1 1
576.1.h $$\chi_{576}(161, \cdot)$$ None 0 1
576.1.j $$\chi_{576}(17, \cdot)$$ None 0 2
576.1.m $$\chi_{576}(271, \cdot)$$ None 0 2
576.1.n $$\chi_{576}(353, \cdot)$$ 576.1.n.a 4 2
576.1.o $$\chi_{576}(319, \cdot)$$ 576.1.o.a 4 2
576.1.q $$\chi_{576}(65, \cdot)$$ None 0 2
576.1.t $$\chi_{576}(31, \cdot)$$ None 0 2
576.1.u $$\chi_{576}(55, \cdot)$$ None 0 4
576.1.x $$\chi_{576}(89, \cdot)$$ None 0 4
576.1.z $$\chi_{576}(79, \cdot)$$ None 0 4
576.1.ba $$\chi_{576}(113, \cdot)$$ None 0 4
576.1.bc $$\chi_{576}(53, \cdot)$$ None 0 8
576.1.bf $$\chi_{576}(19, \cdot)$$ None 0 8
576.1.bh $$\chi_{576}(7, \cdot)$$ None 0 8
576.1.bi $$\chi_{576}(41, \cdot)$$ None 0 8
576.1.bk $$\chi_{576}(43, \cdot)$$ None 0 16
576.1.bn $$\chi_{576}(5, \cdot)$$ None 0 16

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(576))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(576)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 2}$$