# Properties

 Label 152.4 Level 152 Weight 4 Dimension 1173 Nonzero newspaces 9 Newform subspaces 17 Sturm bound 5760 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$152 = 2^{3} \cdot 19$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$9$$ Newform subspaces: $$17$$ Sturm bound: $$5760$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(152))$$.

Total New Old
Modular forms 2268 1241 1027
Cusp forms 2052 1173 879
Eisenstein series 216 68 148

## Trace form

 $$1173q - 14q^{2} - 10q^{3} + 6q^{4} + 4q^{5} - 74q^{6} - 34q^{7} - 98q^{8} - 10q^{9} + O(q^{10})$$ $$1173q - 14q^{2} - 10q^{3} + 6q^{4} + 4q^{5} - 74q^{6} - 34q^{7} - 98q^{8} - 10q^{9} + 94q^{10} + 70q^{11} + 94q^{12} - 44q^{13} - 50q^{14} - 258q^{15} - 50q^{16} - 80q^{17} - 22q^{18} - 62q^{19} - 260q^{20} + 192q^{21} + 150q^{22} + 702q^{23} + 206q^{24} + 154q^{25} - 578q^{26} - 979q^{27} - 210q^{28} - 1026q^{29} + 206q^{30} - 684q^{31} + 686q^{32} + 194q^{33} - 74q^{34} + 1194q^{35} - 42q^{36} + 990q^{37} + 178q^{38} + 3150q^{39} - 466q^{40} + 1090q^{41} + 430q^{42} + 130q^{43} - 354q^{44} - 1070q^{45} - 626q^{46} - 3372q^{47} - 1362q^{48} - 1096q^{49} + 34q^{50} - 923q^{51} + 1102q^{52} + 484q^{53} - 988q^{54} + 478q^{55} + 622q^{56} - 252q^{57} + 1644q^{58} + 1318q^{59} + 7266q^{60} + 1330q^{61} + 10508q^{62} + 6310q^{63} + 7038q^{64} - 298q^{65} + 2478q^{66} - 718q^{67} - 2748q^{68} - 448q^{69} - 10634q^{70} - 4156q^{71} - 16948q^{72} - 4757q^{73} - 13106q^{74} - 10418q^{75} - 13910q^{76} - 1830q^{77} - 13558q^{78} - 4788q^{79} - 5250q^{80} - 39q^{81} - 9208q^{82} - 1516q^{83} - 1562q^{84} + 200q^{85} + 9040q^{86} + 4362q^{87} + 10974q^{88} + 3250q^{89} + 19310q^{90} + 10806q^{91} + 14064q^{92} + 2878q^{93} + 10938q^{94} - 7390q^{95} + 860q^{96} - 8780q^{97} - 1134q^{98} - 7097q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(152))$$

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
152.4.a $$\chi_{152}(1, \cdot)$$ 152.4.a.a 2 1
152.4.a.b 3
152.4.a.c 3
152.4.a.d 5
152.4.b $$\chi_{152}(75, \cdot)$$ 152.4.b.a 2 1
152.4.b.b 56
152.4.c $$\chi_{152}(77, \cdot)$$ 152.4.c.a 54 1
152.4.h $$\chi_{152}(151, \cdot)$$ None 0 1
152.4.i $$\chi_{152}(49, \cdot)$$ 152.4.i.a 14 2
152.4.i.b 16
152.4.j $$\chi_{152}(31, \cdot)$$ None 0 2
152.4.o $$\chi_{152}(27, \cdot)$$ 152.4.o.a 4 2
152.4.o.b 112
152.4.p $$\chi_{152}(45, \cdot)$$ 152.4.p.a 116 2
152.4.q $$\chi_{152}(9, \cdot)$$ 152.4.q.a 42 6
152.4.q.b 48
152.4.t $$\chi_{152}(5, \cdot)$$ 152.4.t.a 348 6
152.4.v $$\chi_{152}(3, \cdot)$$ 152.4.v.a 12 6
152.4.v.b 336
152.4.w $$\chi_{152}(15, \cdot)$$ None 0 6

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(152))$$ into lower level spaces

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