# Properties

 Label 608.1 Level 608 Weight 1 Dimension 14 Nonzero newspaces 4 Newform subspaces 5 Sturm bound 23040 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$608 = 2^{5} \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$23040$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(608))$$.

Total New Old
Modular forms 626 184 442
Cusp forms 50 14 36
Eisenstein series 576 170 406

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 10 4 0 0

## Trace form

 $$14 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 3 q^{9} + O(q^{10})$$ $$14 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 3 q^{9} + 2 q^{11} - 2 q^{13} - 6 q^{17} + q^{19} + 2 q^{23} + q^{25} - 5 q^{27} - 2 q^{29} - 4 q^{33} - 2 q^{39} - 4 q^{41} + 2 q^{43} - 4 q^{47} + 3 q^{49} - 5 q^{51} + 2 q^{53} - 6 q^{57} + 2 q^{59} + 2 q^{61} - 4 q^{65} + 2 q^{67} - 4 q^{69} + 7 q^{73} + 2 q^{75} + 4 q^{81} + 2 q^{83} + 2 q^{85} - 2 q^{87} - 4 q^{89} - 4 q^{93} - 4 q^{97} - 3 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(608))$$

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
608.1.d $$\chi_{608}(191, \cdot)$$ None 0 1
608.1.e $$\chi_{608}(417, \cdot)$$ None 0 1
608.1.f $$\chi_{608}(495, \cdot)$$ None 0 1
608.1.g $$\chi_{608}(113, \cdot)$$ 608.1.g.a 1 1
608.1.g.b 1
608.1.j $$\chi_{608}(265, \cdot)$$ None 0 2
608.1.l $$\chi_{608}(39, \cdot)$$ None 0 2
608.1.o $$\chi_{608}(239, \cdot)$$ 608.1.o.a 2 2
608.1.p $$\chi_{608}(145, \cdot)$$ None 0 2
608.1.q $$\chi_{608}(159, \cdot)$$ 608.1.q.a 4 2
608.1.r $$\chi_{608}(65, \cdot)$$ None 0 2
608.1.w $$\chi_{608}(37, \cdot)$$ None 0 4
608.1.x $$\chi_{608}(115, \cdot)$$ None 0 4
608.1.ba $$\chi_{608}(217, \cdot)$$ None 0 4
608.1.bc $$\chi_{608}(7, \cdot)$$ None 0 4
608.1.bd $$\chi_{608}(33, \cdot)$$ None 0 6
608.1.be $$\chi_{608}(241, \cdot)$$ None 0 6
608.1.bg $$\chi_{608}(47, \cdot)$$ 608.1.bg.a 6 6
608.1.bj $$\chi_{608}(63, \cdot)$$ None 0 6
608.1.bk $$\chi_{608}(11, \cdot)$$ None 0 8
608.1.bl $$\chi_{608}(69, \cdot)$$ None 0 8
608.1.bp $$\chi_{608}(23, \cdot)$$ None 0 12
608.1.br $$\chi_{608}(41, \cdot)$$ None 0 12
608.1.bu $$\chi_{608}(35, \cdot)$$ None 0 24
608.1.bv $$\chi_{608}(13, \cdot)$$ None 0 24

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(608))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(608)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 2}$$