## Defining parameters

 Level: $$N$$ = $$152 = 2^{3} \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$4$$ Sturm bound: $$1440$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(152))$$.

Total New Old
Modular forms 120 44 76
Cusp forms 12 10 2
Eisenstein series 108 34 74

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 10 0 0 0

## Trace form

 $$10q - q^{2} - 2q^{3} + q^{4} - 4q^{6} - 2q^{7} - q^{8} - 3q^{9} + O(q^{10})$$ $$10q - q^{2} - 2q^{3} + q^{4} - 4q^{6} - 2q^{7} - q^{8} - 3q^{9} - 2q^{11} - 2q^{12} + q^{16} - 4q^{17} + 6q^{18} - q^{19} + 7q^{22} - 2q^{23} - 4q^{24} + q^{25} - 2q^{26} + 5q^{27} - 2q^{28} - q^{32} - 4q^{33} - 2q^{34} - 3q^{36} + q^{38} + 2q^{39} - 2q^{41} + 2q^{42} - 2q^{43} + 7q^{44} + 4q^{47} + 7q^{48} - q^{49} - q^{50} + 5q^{51} - 2q^{54} - 4q^{57} - 2q^{58} - 2q^{59} + q^{64} - 4q^{66} - 2q^{67} + 5q^{68} + 6q^{72} + 5q^{73} + 4q^{74} - 2q^{75} - q^{76} + 2q^{81} - 2q^{82} - 2q^{83} - 2q^{86} + 2q^{87} - 2q^{88} - 2q^{89} - 2q^{92} - 4q^{96} - 2q^{97} - q^{98} + 3q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(152))$$

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
152.1.d $$\chi_{152}(39, \cdot)$$ None 0 1
152.1.e $$\chi_{152}(113, \cdot)$$ None 0 1
152.1.f $$\chi_{152}(115, \cdot)$$ None 0 1
152.1.g $$\chi_{152}(37, \cdot)$$ 152.1.g.a 1 1
152.1.g.b 1
152.1.k $$\chi_{152}(11, \cdot)$$ 152.1.k.a 2 2
152.1.l $$\chi_{152}(69, \cdot)$$ None 0 2
152.1.m $$\chi_{152}(7, \cdot)$$ None 0 2
152.1.n $$\chi_{152}(65, \cdot)$$ None 0 2
152.1.r $$\chi_{152}(33, \cdot)$$ None 0 6
152.1.s $$\chi_{152}(13, \cdot)$$ None 0 6
152.1.u $$\chi_{152}(35, \cdot)$$ 152.1.u.a 6 6
152.1.x $$\chi_{152}(23, \cdot)$$ None 0 6

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(152))$$ into lower level spaces

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