# Properties

 Label 152.3 Level 152 Weight 3 Dimension 772 Nonzero newspaces 9 Newform subspaces 14 Sturm bound 4320 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$152 = 2^{3} \cdot 19$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$9$$ Newform subspaces: $$14$$ Sturm bound: $$4320$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(152))$$.

Total New Old
Modular forms 1548 840 708
Cusp forms 1332 772 560
Eisenstein series 216 68 148

## Trace form

 $$772q - 14q^{2} - 14q^{3} - 26q^{4} - 26q^{6} - 18q^{7} - 2q^{8} - 26q^{9} + O(q^{10})$$ $$772q - 14q^{2} - 14q^{3} - 26q^{4} - 26q^{6} - 18q^{7} - 2q^{8} - 26q^{9} - 18q^{10} - 46q^{11} - 2q^{12} - 18q^{14} - 18q^{15} - 50q^{16} - 40q^{17} - 38q^{18} + 16q^{19} - 36q^{20} + 38q^{22} - 18q^{23} - 50q^{24} - 86q^{25} - 18q^{26} + 16q^{27} - 18q^{28} + 144q^{29} - 18q^{30} + 90q^{31} + 46q^{32} + 236q^{33} - 10q^{34} + 54q^{35} + 22q^{36} - 86q^{38} - 144q^{39} - 18q^{40} - 16q^{41} - 18q^{42} - 262q^{43} - 130q^{44} - 432q^{45} - 18q^{46} - 198q^{47} + 46q^{48} - 350q^{49} + 82q^{50} - 136q^{51} - 18q^{52} - 68q^{54} - 18q^{55} - 18q^{56} - 104q^{57} - 36q^{58} + 146q^{59} - 558q^{60} - 252q^{61} - 1188q^{62} - 882q^{63} - 1730q^{64} - 576q^{65} - 1426q^{66} - 1006q^{67} - 916q^{68} - 1098q^{70} - 234q^{71} - 908q^{72} + 86q^{73} - 162q^{74} + 64q^{75} + 298q^{76} + 108q^{77} + 522q^{78} + 486q^{79} + 702q^{80} + 472q^{81} + 1688q^{82} + 98q^{83} + 1926q^{84} + 1424q^{86} + 1278q^{87} + 2078q^{88} + 428q^{89} + 2142q^{90} + 1134q^{91} + 1512q^{92} + 324q^{93} + 666q^{94} + 630q^{95} - 164q^{96} + 728q^{97} + 178q^{98} + 1004q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(152))$$

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
152.3.d $$\chi_{152}(39, \cdot)$$ None 0 1
152.3.e $$\chi_{152}(113, \cdot)$$ 152.3.e.a 2 1
152.3.e.b 8
152.3.f $$\chi_{152}(115, \cdot)$$ 152.3.f.a 36 1
152.3.g $$\chi_{152}(37, \cdot)$$ 152.3.g.a 3 1
152.3.g.b 3
152.3.g.c 32
152.3.k $$\chi_{152}(11, \cdot)$$ 152.3.k.a 4 2
152.3.k.b 72
152.3.l $$\chi_{152}(69, \cdot)$$ 152.3.l.a 76 2
152.3.m $$\chi_{152}(7, \cdot)$$ None 0 2
152.3.n $$\chi_{152}(65, \cdot)$$ 152.3.n.a 20 2
152.3.r $$\chi_{152}(33, \cdot)$$ 152.3.r.a 60 6
152.3.s $$\chi_{152}(13, \cdot)$$ 152.3.s.a 228 6
152.3.u $$\chi_{152}(35, \cdot)$$ 152.3.u.a 12 6
152.3.u.b 216
152.3.x $$\chi_{152}(23, \cdot)$$ None 0 6

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(152))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(152)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 2}$$