# Properties

 Label 912.1 Level 912 Weight 1 Dimension 26 Nonzero newspaces 5 Newform subspaces 8 Sturm bound 46080 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$5$$ Newform subspaces: $$8$$ Sturm bound: $$46080$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(912))$$.

Total New Old
Modular forms 1146 178 968
Cusp forms 138 26 112
Eisenstein series 1008 152 856

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 26 0 0 0

## Trace form

 $$26 q + q^{3} + 2 q^{7} - q^{9} + O(q^{10})$$ $$26 q + q^{3} + 2 q^{7} - q^{9} - 2 q^{13} + q^{19} - 2 q^{21} - q^{25} + q^{27} + 2 q^{31} - 2 q^{37} + 2 q^{39} + 2 q^{43} - 3 q^{49} - q^{57} - 11 q^{61} - 7 q^{63} + 2 q^{67} - 2 q^{73} - 8 q^{75} - 7 q^{79} - q^{81} - 5 q^{91} - 11 q^{93} - 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(912))$$

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
912.1.b $$\chi_{912}(911, \cdot)$$ 912.1.b.a 1 1
912.1.b.b 1
912.1.c $$\chi_{912}(343, \cdot)$$ None 0 1
912.1.h $$\chi_{912}(305, \cdot)$$ None 0 1
912.1.i $$\chi_{912}(265, \cdot)$$ None 0 1
912.1.l $$\chi_{912}(455, \cdot)$$ None 0 1
912.1.m $$\chi_{912}(799, \cdot)$$ None 0 1
912.1.n $$\chi_{912}(761, \cdot)$$ None 0 1
912.1.o $$\chi_{912}(721, \cdot)$$ None 0 1
912.1.s $$\chi_{912}(77, \cdot)$$ None 0 2
912.1.t $$\chi_{912}(37, \cdot)$$ None 0 2
912.1.w $$\chi_{912}(227, \cdot)$$ None 0 2
912.1.x $$\chi_{912}(115, \cdot)$$ None 0 2
912.1.z $$\chi_{912}(463, \cdot)$$ None 0 2
912.1.ba $$\chi_{912}(407, \cdot)$$ None 0 2
912.1.be $$\chi_{912}(145, \cdot)$$ None 0 2
912.1.bf $$\chi_{912}(425, \cdot)$$ None 0 2
912.1.bi $$\chi_{912}(7, \cdot)$$ None 0 2
912.1.bj $$\chi_{912}(335, \cdot)$$ 912.1.bj.a 2 2
912.1.bj.b 2
912.1.bk $$\chi_{912}(217, \cdot)$$ None 0 2
912.1.bl $$\chi_{912}(353, \cdot)$$ 912.1.bl.a 2 2
912.1.bp $$\chi_{912}(373, \cdot)$$ None 0 4
912.1.bs $$\chi_{912}(125, \cdot)$$ None 0 4
912.1.bt $$\chi_{912}(163, \cdot)$$ None 0 4
912.1.bw $$\chi_{912}(107, \cdot)$$ None 0 4
912.1.bx $$\chi_{912}(137, \cdot)$$ None 0 6
912.1.by $$\chi_{912}(97, \cdot)$$ None 0 6
912.1.cb $$\chi_{912}(17, \cdot)$$ 912.1.cb.a 6 6
912.1.cd $$\chi_{912}(409, \cdot)$$ None 0 6
912.1.ce $$\chi_{912}(143, \cdot)$$ 912.1.ce.a 6 6
912.1.ce.b 6
912.1.cg $$\chi_{912}(55, \cdot)$$ None 0 6
912.1.cj $$\chi_{912}(71, \cdot)$$ None 0 6
912.1.cl $$\chi_{912}(175, \cdot)$$ None 0 6
912.1.cm $$\chi_{912}(59, \cdot)$$ None 0 12
912.1.co $$\chi_{912}(43, \cdot)$$ None 0 12
912.1.cr $$\chi_{912}(5, \cdot)$$ None 0 12
912.1.ct $$\chi_{912}(13, \cdot)$$ None 0 12

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(912))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(912)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 2}$$