Properties

Label 115.6
Level 115
Weight 6
Dimension 2348
Nonzero newspaces 6
Sturm bound 6336
Trace bound 1

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Defining parameters

Level: \( N \) = \( 115 = 5 \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(6336\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(115))\).

Total New Old
Modular forms 2728 2476 252
Cusp forms 2552 2348 204
Eisenstein series 176 128 48

Trace form

\( 2348 q - 26 q^{2} - 14 q^{3} + 82 q^{4} + 97 q^{5} - 578 q^{6} - 406 q^{7} + 218 q^{8} + 1044 q^{9} + O(q^{10}) \) \( 2348 q - 26 q^{2} - 14 q^{3} + 82 q^{4} + 97 q^{5} - 578 q^{6} - 406 q^{7} + 218 q^{8} + 1044 q^{9} + 747 q^{10} - 778 q^{11} - 246 q^{12} - 594 q^{13} - 2374 q^{14} + 2158 q^{15} - 4066 q^{16} - 4608 q^{17} - 24106 q^{18} - 2824 q^{19} + 6951 q^{20} + 31236 q^{21} + 21888 q^{22} + 17286 q^{23} + 28564 q^{24} - 4301 q^{25} - 18282 q^{26} - 48068 q^{27} - 72342 q^{28} + 12056 q^{29} - 9489 q^{30} - 22420 q^{31} + 52330 q^{32} + 81316 q^{33} + 140406 q^{34} - 1603 q^{35} - 118132 q^{36} - 144618 q^{37} - 195772 q^{38} - 110990 q^{39} - 44633 q^{40} + 18158 q^{41} + 159470 q^{42} + 121178 q^{43} + 282460 q^{44} + 117438 q^{45} + 374582 q^{46} + 170300 q^{47} + 197594 q^{48} - 52848 q^{49} - 95483 q^{50} - 100346 q^{51} - 542586 q^{52} - 191638 q^{53} - 275062 q^{54} - 18751 q^{55} - 308516 q^{56} - 232640 q^{57} - 64460 q^{58} + 77718 q^{59} - 92643 q^{60} - 292238 q^{61} - 195622 q^{62} + 72736 q^{63} + 298602 q^{64} + 166254 q^{65} + 499936 q^{66} + 66750 q^{67} + 1126768 q^{68} + 416044 q^{69} + 410702 q^{70} + 204372 q^{71} + 474620 q^{72} + 98602 q^{73} + 701644 q^{74} + 608328 q^{75} - 220876 q^{76} - 709428 q^{77} - 2039378 q^{78} - 1456230 q^{79} - 1868894 q^{80} - 2370328 q^{81} - 1109730 q^{82} - 370868 q^{83} + 76078 q^{84} + 294979 q^{85} + 1605762 q^{86} + 936034 q^{87} + 900954 q^{88} + 743906 q^{89} + 1525058 q^{90} + 1376100 q^{91} + 1704728 q^{92} + 1973308 q^{93} + 1032412 q^{94} - 880398 q^{95} - 340352 q^{96} - 314564 q^{97} - 491914 q^{98} - 558404 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(115))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
115.6.a \(\chi_{115}(1, \cdot)\) 115.6.a.a 2 1
115.6.a.b 7
115.6.a.c 7
115.6.a.d 10
115.6.a.e 12
115.6.b \(\chi_{115}(24, \cdot)\) 115.6.b.a 54 1
115.6.e \(\chi_{115}(22, \cdot)\) n/a 116 2
115.6.g \(\chi_{115}(6, \cdot)\) n/a 400 10
115.6.j \(\chi_{115}(4, \cdot)\) n/a 580 10
115.6.l \(\chi_{115}(7, \cdot)\) n/a 1160 20

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(115))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(115)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)