# Properties

 Label 152.5 Level 152 Weight 5 Dimension 1578 Nonzero newspaces 9 Newform subspaces 13 Sturm bound 7200 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$152 = 2^{3} \cdot 19$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$9$$ Newform subspaces: $$13$$ Sturm bound: $$7200$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(152))$$.

Total New Old
Modular forms 2988 1646 1342
Cusp forms 2772 1578 1194
Eisenstein series 216 68 148

## Trace form

 $$1578q - 22q^{2} - 14q^{3} + 6q^{4} + 118q^{6} - 18q^{7} - 322q^{8} - 86q^{9} + O(q^{10})$$ $$1578q - 22q^{2} - 14q^{3} + 6q^{4} + 118q^{6} - 18q^{7} - 322q^{8} - 86q^{9} - 498q^{10} + 178q^{11} + 766q^{12} + 942q^{14} - 18q^{15} - 1074q^{16} + 208q^{17} - 1118q^{18} - 720q^{19} + 924q^{20} + 246q^{22} - 18q^{23} + 718q^{24} + 54q^{25} + 462q^{26} + 8098q^{27} - 1938q^{28} + 864q^{29} - 2898q^{30} - 2826q^{31} + 1838q^{32} - 11500q^{33} + 5478q^{34} - 12450q^{35} - 6218q^{36} - 1486q^{38} + 7956q^{39} + 5742q^{40} + 3232q^{41} + 5742q^{42} + 25314q^{43} - 2q^{44} + 11232q^{45} - 4818q^{46} - 1098q^{47} + 3886q^{48} - 9018q^{49} - 6358q^{50} - 33358q^{51} - 978q^{52} - 692q^{54} - 18q^{55} - 11538q^{56} + 4432q^{57} - 5316q^{58} + 20530q^{59} - 50958q^{60} - 18648q^{61} - 33468q^{62} - 15570q^{63} + 3774q^{64} + 12324q^{65} + 60302q^{66} + 38706q^{67} + 107740q^{68} + 131862q^{70} + 27198q^{71} + 102532q^{72} + 2412q^{73} - 6210q^{74} + 25504q^{75} - 30390q^{76} - 16200q^{77} - 76518q^{78} - 71586q^{79} - 124098q^{80} - 52406q^{81} - 203424q^{82} - 57518q^{83} - 180666q^{84} - 50216q^{86} - 38898q^{87} - 2658q^{88} + 42808q^{89} + 118782q^{90} + 92910q^{91} + 170232q^{92} + 44712q^{93} + 85674q^{94} + 86814q^{95} + 52060q^{96} + 20688q^{97} - 24982q^{98} + 4118q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(152))$$

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
152.5.d $$\chi_{152}(39, \cdot)$$ None 0 1
152.5.e $$\chi_{152}(113, \cdot)$$ 152.5.e.a 20 1
152.5.f $$\chi_{152}(115, \cdot)$$ 152.5.f.a 72 1
152.5.g $$\chi_{152}(37, \cdot)$$ 152.5.g.a 3 1
152.5.g.b 3
152.5.g.c 72
152.5.k $$\chi_{152}(11, \cdot)$$ 152.5.k.a 4 2
152.5.k.b 152
152.5.l $$\chi_{152}(69, \cdot)$$ 152.5.l.a 156 2
152.5.m $$\chi_{152}(7, \cdot)$$ None 0 2
152.5.n $$\chi_{152}(65, \cdot)$$ 152.5.n.a 40 2
152.5.r $$\chi_{152}(33, \cdot)$$ 152.5.r.a 120 6
152.5.s $$\chi_{152}(13, \cdot)$$ 152.5.s.a 468 6
152.5.u $$\chi_{152}(35, \cdot)$$ 152.5.u.a 12 6
152.5.u.b 456
152.5.x $$\chi_{152}(23, \cdot)$$ None 0 6

## Decomposition of $$S_{5}^{\mathrm{old}}(\Gamma_1(152))$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(\Gamma_1(152)) \cong$$ $$S_{5}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 2}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 3}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 2}$$