## Defining parameters

 Level: $$N$$ = $$152 = 2^{3} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$9$$ Newform subspaces: $$21$$ Sturm bound: $$2880$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(152))$$.

Total New Old
Modular forms 828 437 391
Cusp forms 613 369 244
Eisenstein series 215 68 147

## Trace form

 $$369q - 18q^{2} - 18q^{3} - 18q^{4} - 18q^{6} - 18q^{7} - 18q^{8} - 36q^{9} + O(q^{10})$$ $$369q - 18q^{2} - 18q^{3} - 18q^{4} - 18q^{6} - 18q^{7} - 18q^{8} - 36q^{9} - 18q^{10} - 18q^{11} - 18q^{12} - 18q^{14} - 18q^{15} - 18q^{16} - 36q^{17} - 18q^{18} - 18q^{19} - 36q^{20} - 18q^{22} - 18q^{23} - 18q^{24} - 36q^{25} - 18q^{26} - 27q^{27} - 18q^{28} - 18q^{29} - 18q^{30} - 36q^{31} - 18q^{32} - 90q^{33} - 18q^{34} - 54q^{35} - 18q^{36} - 18q^{37} - 18q^{38} - 90q^{39} - 18q^{40} - 54q^{41} - 18q^{42} - 54q^{43} - 18q^{44} - 54q^{45} - 18q^{46} - 36q^{47} - 18q^{48} - 54q^{49} - 18q^{50} - 27q^{51} - 18q^{52} + 36q^{54} - 18q^{55} - 18q^{56} - 36q^{57} - 36q^{58} - 18q^{59} + 18q^{60} + 18q^{61} + 72q^{62} + 54q^{63} + 126q^{64} + 18q^{65} + 126q^{66} + 90q^{67} + 108q^{68} + 198q^{70} + 36q^{71} + 252q^{72} + 45q^{73} + 126q^{74} + 126q^{75} + 162q^{76} + 54q^{77} + 162q^{78} + 108q^{79} + 126q^{80} + 45q^{81} + 252q^{82} + 36q^{83} + 198q^{84} + 108q^{86} + 90q^{87} + 126q^{88} + 18q^{89} + 126q^{90} + 54q^{91} + 72q^{92} + 18q^{93} + 18q^{94} - 54q^{95} - 36q^{96} - 72q^{97} - 18q^{98} - 81q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$

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
152.2.a $$\chi_{152}(1, \cdot)$$ 152.2.a.a 1 1
152.2.a.b 1
152.2.a.c 3
152.2.b $$\chi_{152}(75, \cdot)$$ 152.2.b.a 2 1
152.2.b.b 4
152.2.b.c 12
152.2.c $$\chi_{152}(77, \cdot)$$ 152.2.c.a 2 1
152.2.c.b 16
152.2.h $$\chi_{152}(151, \cdot)$$ None 0 1
152.2.i $$\chi_{152}(49, \cdot)$$ 152.2.i.a 2 2
152.2.i.b 2
152.2.i.c 6
152.2.j $$\chi_{152}(31, \cdot)$$ None 0 2
152.2.o $$\chi_{152}(27, \cdot)$$ 152.2.o.a 4 2
152.2.o.b 4
152.2.o.c 28
152.2.p $$\chi_{152}(45, \cdot)$$ 152.2.p.a 36 2
152.2.q $$\chi_{152}(9, \cdot)$$ 152.2.q.a 6 6
152.2.q.b 6
152.2.q.c 18
152.2.t $$\chi_{152}(5, \cdot)$$ 152.2.t.a 108 6
152.2.v $$\chi_{152}(3, \cdot)$$ 152.2.v.a 12 6
152.2.v.b 96
152.2.w $$\chi_{152}(15, \cdot)$$ None 0 6

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(152))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(152)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 2}$$