## Defining parameters

 Level: $$N$$ = $$2888 = 2^{3} \cdot 19^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$8$$ Newform subspaces: $$21$$ Sturm bound: $$519840$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2888))$$.

Total New Old
Modular forms 3414 1179 2235
Cusp forms 390 242 148
Eisenstein series 3024 937 2087

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 242 0 0 0

## Trace form

 $$242 q + q^{2} + 2 q^{3} - q^{4} + 4 q^{6} + 2 q^{7} + q^{8} + 3 q^{9} + O(q^{10})$$ $$242 q + q^{2} + 2 q^{3} - q^{4} + 4 q^{6} + 2 q^{7} + q^{8} + 3 q^{9} + 2 q^{11} + 2 q^{12} - q^{16} + 4 q^{17} - 15 q^{18} - 16 q^{22} + 2 q^{23} + 4 q^{24} - q^{25} + 2 q^{26} - 14 q^{27} + 2 q^{28} + q^{32} + 4 q^{33} + 2 q^{34} + 3 q^{36} + 16 q^{39} + 2 q^{41} - 2 q^{42} + 2 q^{43} - 16 q^{44} - 4 q^{47} - 16 q^{48} + q^{49} + q^{50} - 14 q^{51} + 2 q^{54} - 16 q^{58} + 2 q^{59} - q^{64} + 4 q^{66} + 2 q^{67} - 14 q^{68} - 15 q^{72} - 14 q^{73} - 4 q^{74} + 2 q^{75} - 11 q^{81} + 2 q^{82} + 2 q^{83} + 2 q^{86} - 2 q^{87} + 2 q^{88} + 2 q^{89} + 2 q^{92} - 32 q^{96} + 2 q^{97} + q^{98} - 12 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2888))$$

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
2888.1.d $$\chi_{2888}(2167, \cdot)$$ None 0 1
2888.1.e $$\chi_{2888}(721, \cdot)$$ None 0 1
2888.1.f $$\chi_{2888}(723, \cdot)$$ 2888.1.f.a 1 1
2888.1.f.b 1
2888.1.f.c 3
2888.1.f.d 3
2888.1.g $$\chi_{2888}(2165, \cdot)$$ None 0 1
2888.1.k $$\chi_{2888}(2595, \cdot)$$ 2888.1.k.a 2 2
2888.1.k.b 6
2888.1.k.c 6
2888.1.l $$\chi_{2888}(69, \cdot)$$ 2888.1.l.a 2 2
2888.1.l.b 2
2888.1.m $$\chi_{2888}(1151, \cdot)$$ None 0 2
2888.1.n $$\chi_{2888}(1513, \cdot)$$ None 0 2
2888.1.r $$\chi_{2888}(849, \cdot)$$ None 0 6
2888.1.s $$\chi_{2888}(333, \cdot)$$ 2888.1.s.a 6 6
2888.1.s.b 6
2888.1.u $$\chi_{2888}(99, \cdot)$$ 2888.1.u.a 6 6
2888.1.u.b 6
2888.1.u.c 6
2888.1.u.d 6
2888.1.u.e 6
2888.1.u.f 6
2888.1.u.g 6
2888.1.x $$\chi_{2888}(415, \cdot)$$ None 0 6
2888.1.ba $$\chi_{2888}(37, \cdot)$$ None 0 18
2888.1.bb $$\chi_{2888}(115, \cdot)$$ 2888.1.bb.a 18 18
2888.1.bc $$\chi_{2888}(113, \cdot)$$ None 0 18
2888.1.bd $$\chi_{2888}(39, \cdot)$$ None 0 18
2888.1.bj $$\chi_{2888}(65, \cdot)$$ None 0 36
2888.1.bk $$\chi_{2888}(7, \cdot)$$ None 0 36
2888.1.bl $$\chi_{2888}(141, \cdot)$$ None 0 36
2888.1.bm $$\chi_{2888}(11, \cdot)$$ 2888.1.bm.a 36 36
2888.1.bp $$\chi_{2888}(23, \cdot)$$ None 0 108
2888.1.bs $$\chi_{2888}(35, \cdot)$$ 2888.1.bs.a 108 108
2888.1.bu $$\chi_{2888}(13, \cdot)$$ None 0 108
2888.1.bv $$\chi_{2888}(33, \cdot)$$ None 0 108

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(2888))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(2888)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1444))$$$$^{\oplus 2}$$