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Properties

Label 116.6
Level 116
Weight 6
Dimension 1195
Nonzero newspaces 6
Sturm bound 5040
Trace bound 1

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Defining parameters

Level: \( N \) = \( 116 = 2^{2} \cdot 29 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(5040\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(116))\).

Total New Old
Modular forms 2170 1251 919
Cusp forms 2030 1195 835
Eisenstein series 140 56 84

Trace form

\( 1195 q - 14 q^{2} + 24 q^{3} - 14 q^{4} - 136 q^{5} - 14 q^{6} + 176 q^{7} - 14 q^{8} + 170 q^{9} + O(q^{10}) \) \( 1195 q - 14 q^{2} + 24 q^{3} - 14 q^{4} - 136 q^{5} - 14 q^{6} + 176 q^{7} - 14 q^{8} + 170 q^{9} - 14 q^{10} - 1080 q^{11} - 14 q^{12} + 808 q^{13} - 14 q^{14} + 1296 q^{15} - 14 q^{16} - 1216 q^{17} - 14 q^{18} - 1672 q^{19} - 14 q^{20} + 4720 q^{21} - 14 q^{22} + 16202 q^{23} - 14 q^{24} - 478 q^{25} - 14 q^{26} - 35466 q^{27} - 20574 q^{29} - 28 q^{30} - 14252 q^{31} - 14 q^{32} + 44894 q^{33} - 14 q^{34} + 52036 q^{35} - 14 q^{36} + 15422 q^{37} - 14 q^{38} - 66172 q^{39} - 14 q^{40} - 34480 q^{41} - 14 q^{42} + 24200 q^{43} + 114632 q^{44} + 126899 q^{45} + 4116 q^{46} - 50356 q^{47} - 313502 q^{48} - 144918 q^{49} - 240016 q^{50} - 75960 q^{51} - 63966 q^{52} - 6193 q^{53} + 193900 q^{54} + 208352 q^{55} + 290948 q^{56} + 202008 q^{57} + 536074 q^{58} + 93428 q^{59} + 346234 q^{60} + 128192 q^{61} - 17752 q^{62} - 189792 q^{63} - 366800 q^{64} - 216901 q^{65} - 573566 q^{66} - 357840 q^{67} - 531076 q^{68} - 339940 q^{69} - 227262 q^{70} - 183526 q^{71} + 504616 q^{72} + 470271 q^{73} + 347732 q^{74} + 482114 q^{75} - 14 q^{76} + 530482 q^{77} - 14 q^{78} + 237012 q^{79} - 14 q^{80} - 74078 q^{81} - 14 q^{82} - 400256 q^{83} - 3416 q^{84} - 649744 q^{85} - 518758 q^{87} - 28 q^{88} - 451466 q^{89} + 3388 q^{90} - 248372 q^{91} - 14 q^{92} + 248892 q^{93} - 14 q^{94} + 749600 q^{95} - 1493912 q^{96} + 2105053 q^{97} - 571144 q^{98} + 896170 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(116))\)

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
116.6.a \(\chi_{116}(1, \cdot)\) 116.6.a.a 1 1
116.6.a.b 2
116.6.a.c 2
116.6.a.d 6
116.6.c \(\chi_{116}(57, \cdot)\) 116.6.c.a 12 1
116.6.e \(\chi_{116}(75, \cdot)\) n/a 146 2
116.6.g \(\chi_{116}(25, \cdot)\) 116.6.g.a 78 6
116.6.i \(\chi_{116}(5, \cdot)\) 116.6.i.a 72 6
116.6.l \(\chi_{116}(3, \cdot)\) n/a 876 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(116))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(116)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 1}\)