Properties

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

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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

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