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Properties

Label 152.8
Level 152
Weight 8
Dimension 2783
Nonzero newspaces 9
Sturm bound 11520
Trace bound 3

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Defining parameters

Level: \( N \) = \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 9 \)
Sturm bound: \(11520\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(152))\).

Total New Old
Modular forms 5148 2851 2297
Cusp forms 4932 2783 2149
Eisenstein series 216 68 148

Trace form

\( 2783 q - 30 q^{2} + 62 q^{3} - 250 q^{4} - 696 q^{5} - 554 q^{6} + 4718 q^{7} - 3042 q^{8} - 3436 q^{9} + O(q^{10}) \) \( 2783 q - 30 q^{2} + 62 q^{3} - 250 q^{4} - 696 q^{5} - 554 q^{6} + 4718 q^{7} - 3042 q^{8} - 3436 q^{9} + 3294 q^{10} + 11358 q^{11} + 8158 q^{12} + 9320 q^{13} - 24114 q^{14} - 87378 q^{15} - 70706 q^{16} + 51900 q^{17} + 178106 q^{18} + 1334 q^{19} + 229500 q^{20} + 31104 q^{21} - 305738 q^{22} - 163986 q^{23} - 565042 q^{24} + 7844 q^{25} + 633918 q^{26} + 55649 q^{27} + 961582 q^{28} + 152706 q^{29} - 1643314 q^{30} - 667316 q^{31} - 1634130 q^{32} - 1898398 q^{33} + 2018198 q^{34} + 1561434 q^{35} + 2507094 q^{36} + 1855314 q^{37} - 974142 q^{38} - 295674 q^{39} - 1908946 q^{40} - 1479810 q^{41} + 2186158 q^{42} - 3204886 q^{43} + 2192670 q^{44} - 444650 q^{45} - 1859698 q^{46} - 25428 q^{47} - 1707858 q^{48} + 3379390 q^{49} + 297234 q^{50} - 6377687 q^{51} - 1647922 q^{52} - 4218360 q^{53} + 2193476 q^{54} + 8847598 q^{55} + 4937838 q^{56} + 2477220 q^{57} - 6261524 q^{58} + 3727134 q^{59} + 19066146 q^{60} - 2697442 q^{61} - 18973572 q^{62} - 34129034 q^{63} - 19503490 q^{64} - 9301818 q^{65} + 12347118 q^{66} + 18552538 q^{67} + 30421860 q^{68} + 13587584 q^{69} + 55610806 q^{70} + 27831252 q^{71} - 10142740 q^{72} - 11095461 q^{73} - 69162546 q^{74} - 74547818 q^{75} - 82087126 q^{76} - 27345342 q^{77} - 12895510 q^{78} - 28716404 q^{79} + 55962750 q^{80} + 26245155 q^{81} + 129424408 q^{82} + 48236844 q^{83} + 123822694 q^{84} + 12163600 q^{85} + 37658880 q^{86} + 64333050 q^{87} - 85030946 q^{88} - 66198138 q^{89} - 170342290 q^{90} - 72297258 q^{91} - 35917488 q^{92} - 7182026 q^{93} + 116707866 q^{94} - 75935670 q^{95} - 42804388 q^{96} + 45299808 q^{97} + 29966466 q^{98} + 81624907 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(152))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
152.8.a \(\chi_{152}(1, \cdot)\) 152.8.a.a 6 1
152.8.a.b 8
152.8.a.c 8
152.8.a.d 9
152.8.b \(\chi_{152}(75, \cdot)\) n/a 138 1
152.8.c \(\chi_{152}(77, \cdot)\) n/a 126 1
152.8.h \(\chi_{152}(151, \cdot)\) None 0 1
152.8.i \(\chi_{152}(49, \cdot)\) 152.8.i.a 34 2
152.8.i.b 36
152.8.j \(\chi_{152}(31, \cdot)\) None 0 2
152.8.o \(\chi_{152}(27, \cdot)\) n/a 276 2
152.8.p \(\chi_{152}(45, \cdot)\) n/a 276 2
152.8.q \(\chi_{152}(9, \cdot)\) n/a 210 6
152.8.t \(\chi_{152}(5, \cdot)\) n/a 828 6
152.8.v \(\chi_{152}(3, \cdot)\) n/a 828 6
152.8.w \(\chi_{152}(15, \cdot)\) None 0 6

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(152))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(152)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 1}\)