## Defining parameters

 Level: $$N$$ = $$927 = 3^{2} \cdot 103$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$4$$ Sturm bound: $$63648$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(927))$$.

Total New Old
Modular forms 885 478 407
Cusp forms 69 23 46
Eisenstein series 816 455 361

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 23 0 0 0

## Trace form

 $$23q + q^{2} + 7q^{4} - 3q^{7} + 2q^{8} + O(q^{10})$$ $$23q + q^{2} + 7q^{4} - 3q^{7} + 2q^{8} + q^{13} + 2q^{14} + 4q^{16} + q^{17} - 3q^{19} + q^{23} + 6q^{25} - 3q^{26} - 6q^{28} + q^{29} - 2q^{32} - 2q^{34} - 3q^{38} + q^{41} - 7q^{46} + 3q^{49} + q^{50} - 5q^{52} - q^{56} - 2q^{58} + q^{59} + q^{61} + 5q^{64} - 2q^{68} - q^{76} + q^{79} - 7q^{82} + q^{83} - 15q^{91} + 3q^{92} - 16q^{97} - 2q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(927))$$

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
927.1.b $$\chi_{927}(413, \cdot)$$ None 0 1
927.1.d $$\chi_{927}(514, \cdot)$$ 927.1.d.a 1 1
927.1.d.b 2
927.1.d.c 4
927.1.i $$\chi_{927}(365, \cdot)$$ None 0 2
927.1.k $$\chi_{927}(205, \cdot)$$ None 0 2
927.1.l $$\chi_{927}(253, \cdot)$$ None 0 2
927.1.m $$\chi_{927}(778, \cdot)$$ None 0 2
927.1.q $$\chi_{927}(104, \cdot)$$ None 0 2
927.1.r $$\chi_{927}(458, \cdot)$$ None 0 2
927.1.s $$\chi_{927}(56, \cdot)$$ None 0 2
927.1.t $$\chi_{927}(160, \cdot)$$ None 0 2
927.1.v $$\chi_{927}(10, \cdot)$$ 927.1.v.a 16 16
927.1.x $$\chi_{927}(8, \cdot)$$ None 0 16
927.1.bc $$\chi_{927}(40, \cdot)$$ None 0 32
927.1.bd $$\chi_{927}(38, \cdot)$$ None 0 32
927.1.be $$\chi_{927}(17, \cdot)$$ None 0 32
927.1.bf $$\chi_{927}(14, \cdot)$$ None 0 32
927.1.bj $$\chi_{927}(70, \cdot)$$ None 0 32
927.1.bk $$\chi_{927}(109, \cdot)$$ None 0 32
927.1.bl $$\chi_{927}(22, \cdot)$$ None 0 32
927.1.bn $$\chi_{927}(2, \cdot)$$ None 0 32

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(927))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(927)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(103))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(309))$$$$^{\oplus 2}$$