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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

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

Display 100 coefficients 10 coefficients

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 available 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

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