Properties

Label 152.7
Level 152
Weight 7
Dimension 2384
Nonzero newspaces 9
Sturm bound 10080
Trace bound 3

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Defining parameters

Level: \( N \) = \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 9 \)
Sturm bound: \(10080\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(152))\).

Total New Old
Modular forms 4428 2452 1976
Cusp forms 4212 2384 1828
Eisenstein series 216 68 148

Trace form

\( 2384q - 6q^{2} - 14q^{3} - 58q^{4} - 74q^{6} - 18q^{7} + 510q^{8} - 1490q^{9} + O(q^{10}) \) \( 2384q - 6q^{2} - 14q^{3} - 58q^{4} - 74q^{6} - 18q^{7} + 510q^{8} - 1490q^{9} + 3822q^{10} + 2706q^{11} - 8642q^{12} - 11538q^{14} - 18q^{15} + 20942q^{16} - 4920q^{17} + 42994q^{18} + 3920q^{19} - 63396q^{20} - 86282q^{22} - 18q^{23} + 123598q^{24} + 16514q^{25} + 119022q^{26} + 59092q^{27} - 119058q^{28} - 115920q^{29} - 180498q^{30} - 30798q^{31} + 163374q^{32} + 351740q^{33} + 136198q^{34} + 325254q^{35} - 151754q^{36} - 46446q^{38} - 427176q^{39} + 26862q^{40} - 226032q^{41} - 76818q^{42} - 385718q^{43} + 224958q^{44} + 582768q^{45} + 426222q^{46} + 391122q^{47} - 652754q^{48} - 178006q^{49} - 465318q^{50} + 145196q^{51} + 508782q^{52} + 977596q^{54} - 18q^{55} - 698898q^{56} - 12536q^{57} - 1032996q^{58} - 1693998q^{59} - 2577198q^{60} - 442260q^{61} + 2942292q^{62} + 3149262q^{63} + 4958270q^{64} + 2206344q^{65} + 839246q^{66} + 2418514q^{67} - 1948884q^{68} - 8269098q^{70} - 2340378q^{71} - 10754540q^{72} - 2104862q^{73} - 2257890q^{74} - 4967936q^{75} + 3152714q^{76} + 1789668q^{77} + 7734522q^{78} + 7017174q^{79} + 10579902q^{80} + 4900732q^{81} + 13631728q^{82} + 7090626q^{83} - 208506q^{84} - 9823608q^{86} - 8643042q^{87} - 12898274q^{88} - 6551292q^{89} - 10530018q^{90} - 10028178q^{91} - 1569048q^{92} + 3367980q^{93} + 12484554q^{94} + 5787270q^{95} + 3520348q^{96} - 4997432q^{97} + 6664890q^{98} + 2763200q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(152))\)

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
152.7.d \(\chi_{152}(39, \cdot)\) None 0 1
152.7.e \(\chi_{152}(113, \cdot)\) 152.7.e.a 30 1
152.7.f \(\chi_{152}(115, \cdot)\) n/a 108 1
152.7.g \(\chi_{152}(37, \cdot)\) n/a 118 1
152.7.k \(\chi_{152}(11, \cdot)\) n/a 236 2
152.7.l \(\chi_{152}(69, \cdot)\) n/a 236 2
152.7.m \(\chi_{152}(7, \cdot)\) None 0 2
152.7.n \(\chi_{152}(65, \cdot)\) 152.7.n.a 60 2
152.7.r \(\chi_{152}(33, \cdot)\) n/a 180 6
152.7.s \(\chi_{152}(13, \cdot)\) n/a 708 6
152.7.u \(\chi_{152}(35, \cdot)\) n/a 708 6
152.7.x \(\chi_{152}(23, \cdot)\) None 0 6

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(152))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(152)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)