## Defining parameters

 Level: $$N$$ = $$176 = 2^{4} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$16$$ Sturm bound: $$3840$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(176))$$.

Total New Old
Modular forms 1100 571 529
Cusp forms 821 491 330
Eisenstein series 279 80 199

## Trace form

 $$491 q - 16 q^{2} - 11 q^{3} - 20 q^{4} - 21 q^{5} - 28 q^{6} - 15 q^{7} - 28 q^{8} - 5 q^{9} + O(q^{10})$$ $$491 q - 16 q^{2} - 11 q^{3} - 20 q^{4} - 21 q^{5} - 28 q^{6} - 15 q^{7} - 28 q^{8} - 5 q^{9} - 20 q^{10} - 17 q^{11} - 32 q^{12} - 21 q^{13} - 12 q^{14} - 23 q^{15} - 4 q^{16} - 37 q^{17} - 24 q^{18} - 27 q^{19} - 28 q^{20} - 38 q^{21} - 20 q^{22} - 30 q^{23} - 20 q^{24} - 5 q^{25} - 28 q^{26} + q^{27} - 36 q^{28} - 37 q^{29} - 12 q^{30} + 17 q^{31} - 36 q^{32} - 61 q^{33} - 48 q^{34} - 37 q^{35} - 12 q^{36} - 57 q^{37} + 4 q^{38} - 75 q^{39} - 4 q^{40} - 45 q^{41} - 20 q^{42} - 60 q^{43} - 16 q^{44} - 114 q^{45} - 44 q^{46} - 77 q^{47} - 36 q^{48} - 97 q^{49} - 8 q^{50} - 83 q^{51} - 12 q^{52} - 25 q^{53} - 20 q^{54} - 45 q^{55} - 24 q^{56} - 25 q^{57} + 4 q^{58} - 3 q^{59} - 20 q^{60} + 11 q^{61} - 52 q^{62} - 8 q^{63} - 20 q^{64} - 58 q^{65} - 24 q^{66} - 10 q^{67} - 20 q^{68} - 16 q^{69} + 104 q^{70} - 5 q^{71} + 72 q^{72} + 75 q^{73} + 80 q^{74} + 13 q^{75} + 116 q^{76} + 51 q^{77} + 208 q^{78} + 35 q^{79} + 184 q^{80} + 55 q^{81} + 180 q^{82} + 39 q^{83} + 236 q^{84} + 127 q^{85} + 140 q^{86} + 70 q^{87} + 292 q^{88} + 70 q^{89} + 308 q^{90} + 37 q^{91} + 188 q^{92} + 103 q^{93} + 252 q^{94} + 59 q^{95} + 212 q^{96} + 83 q^{97} + 212 q^{98} + 37 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(176))$$

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
176.2.a $$\chi_{176}(1, \cdot)$$ 176.2.a.a 1 1
176.2.a.b 1
176.2.a.c 1
176.2.a.d 2
176.2.c $$\chi_{176}(89, \cdot)$$ None 0 1
176.2.e $$\chi_{176}(175, \cdot)$$ 176.2.e.a 2 1
176.2.e.b 4
176.2.g $$\chi_{176}(87, \cdot)$$ None 0 1
176.2.i $$\chi_{176}(43, \cdot)$$ 176.2.i.a 44 2
176.2.j $$\chi_{176}(45, \cdot)$$ 176.2.j.a 40 2
176.2.m $$\chi_{176}(49, \cdot)$$ 176.2.m.a 4 4
176.2.m.b 4
176.2.m.c 4
176.2.m.d 8
176.2.o $$\chi_{176}(7, \cdot)$$ None 0 4
176.2.q $$\chi_{176}(63, \cdot)$$ 176.2.q.a 8 4
176.2.q.b 16
176.2.s $$\chi_{176}(9, \cdot)$$ None 0 4
176.2.w $$\chi_{176}(5, \cdot)$$ 176.2.w.a 176 8
176.2.x $$\chi_{176}(19, \cdot)$$ 176.2.x.a 176 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(176))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(176)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 2}$$