## Defining parameters

 Level: $$N$$ = $$232 = 2^{3} \cdot 29$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$10$$ Newform subspaces: $$15$$ Sturm bound: $$13440$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(232))$$.

Total New Old
Modular forms 5208 2881 2327
Cusp forms 4872 2773 2099
Eisenstein series 336 108 228

## Trace form

 $$2773 q - 24 q^{2} - 20 q^{3} - 4 q^{4} + 4 q^{5} - 84 q^{6} - 44 q^{7} - 108 q^{8} - 30 q^{9} + O(q^{10})$$ $$2773 q - 24 q^{2} - 20 q^{3} - 4 q^{4} + 4 q^{5} - 84 q^{6} - 44 q^{7} - 108 q^{8} - 30 q^{9} + 84 q^{10} + 60 q^{11} + 84 q^{12} - 44 q^{13} - 60 q^{14} - 268 q^{15} - 60 q^{16} - 100 q^{17} - 32 q^{18} - 116 q^{19} - 252 q^{20} + 192 q^{21} + 140 q^{22} + 692 q^{23} + 196 q^{24} + 134 q^{25} - 588 q^{26} - 332 q^{27} - 220 q^{28} - 198 q^{29} + 168 q^{30} - 604 q^{31} + 676 q^{32} - 744 q^{33} - 84 q^{34} + 68 q^{35} - 52 q^{36} + 324 q^{37} + 364 q^{38} + 1268 q^{39} - 476 q^{40} + 620 q^{41} + 420 q^{42} - 132 q^{43} - 364 q^{44} - 3509 q^{45} - 636 q^{46} - 3912 q^{47} - 1372 q^{48} - 246 q^{49} + 24 q^{50} + 1212 q^{51} + 1092 q^{52} + 2815 q^{53} - 1484 q^{54} + 6180 q^{55} + 612 q^{56} + 2704 q^{57} + 812 q^{58} + 2820 q^{59} + 1316 q^{60} + 1420 q^{61} + 868 q^{62} + 3492 q^{63} - 1180 q^{64} - 2145 q^{65} + 308 q^{66} - 2252 q^{67} - 364 q^{68} - 4648 q^{69} - 924 q^{70} - 4696 q^{71} + 52 q^{72} - 5593 q^{73} - 2604 q^{74} - 996 q^{75} - 812 q^{76} + 2112 q^{77} - 1148 q^{78} + 3140 q^{79} + 2660 q^{80} + 3586 q^{81} - 308 q^{82} - 500 q^{83} - 168 q^{84} + 200 q^{85} + 4620 q^{86} - 916 q^{87} - 728 q^{88} - 2548 q^{89} - 140 q^{90} - 1084 q^{91} - 3676 q^{92} - 1280 q^{93} + 1316 q^{94} + 1716 q^{95} + 23128 q^{96} + 1691 q^{97} + 25596 q^{98} + 25380 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(232))$$

We only show spaces with even 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
232.4.a $$\chi_{232}(1, \cdot)$$ 232.4.a.a 3 1
232.4.a.b 3
232.4.a.c 4
232.4.a.d 5
232.4.a.e 6
232.4.c $$\chi_{232}(117, \cdot)$$ 232.4.c.a 84 1
232.4.e $$\chi_{232}(57, \cdot)$$ 232.4.e.a 22 1
232.4.g $$\chi_{232}(173, \cdot)$$ 232.4.g.a 88 1
232.4.i $$\chi_{232}(191, \cdot)$$ None 0 2
232.4.k $$\chi_{232}(75, \cdot)$$ 232.4.k.a 176 2
232.4.m $$\chi_{232}(25, \cdot)$$ 232.4.m.a 66 6
232.4.m.b 72
232.4.o $$\chi_{232}(5, \cdot)$$ 232.4.o.a 528 6
232.4.q $$\chi_{232}(9, \cdot)$$ 232.4.q.a 132 6
232.4.s $$\chi_{232}(45, \cdot)$$ 232.4.s.a 528 6
232.4.v $$\chi_{232}(3, \cdot)$$ 232.4.v.a 1056 12
232.4.x $$\chi_{232}(15, \cdot)$$ None 0 12

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(232))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(232)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(116))$$$$^{\oplus 2}$$