Properties

Label 112.6
Level 112
Weight 6
Dimension 1013
Nonzero newspaces 8
Sturm bound 4608
Trace bound 3

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Defining parameters

Level: \( N \) = \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(4608\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(112))\).

Total New Old
Modular forms 2004 1057 947
Cusp forms 1836 1013 823
Eisenstein series 168 44 124

Trace form

\( 1013 q - 8 q^{2} + 11 q^{3} + 36 q^{4} + 29 q^{5} - 236 q^{6} - 121 q^{7} - 512 q^{8} - 119 q^{9} + O(q^{10}) \) \( 1013 q - 8 q^{2} + 11 q^{3} + 36 q^{4} + 29 q^{5} - 236 q^{6} - 121 q^{7} - 512 q^{8} - 119 q^{9} + 860 q^{10} + 2531 q^{11} - 20 q^{12} - 134 q^{13} + 88 q^{14} - 7866 q^{15} + 1732 q^{16} + 1189 q^{17} + 6264 q^{18} + 7621 q^{19} - 5956 q^{20} + 5297 q^{21} - 8864 q^{22} - 2107 q^{23} - 16748 q^{24} - 12471 q^{25} - 14748 q^{26} - 21166 q^{27} + 7324 q^{28} - 6526 q^{29} + 60876 q^{30} + 26623 q^{31} + 47972 q^{32} + 36277 q^{33} + 3468 q^{34} + 13561 q^{35} - 13808 q^{36} - 1999 q^{37} - 106508 q^{38} - 2582 q^{39} - 150556 q^{40} - 16686 q^{41} + 59900 q^{42} + 12224 q^{43} + 109276 q^{44} - 49140 q^{45} + 34992 q^{46} - 92567 q^{47} + 13852 q^{48} - 305795 q^{49} + 117576 q^{50} - 44419 q^{51} - 34008 q^{52} - 6755 q^{53} + 45484 q^{54} + 112574 q^{55} + 58256 q^{56} + 146074 q^{57} - 55728 q^{58} + 99595 q^{59} + 262524 q^{60} + 127181 q^{61} + 237880 q^{62} - 103839 q^{63} + 156348 q^{64} - 202082 q^{65} - 288620 q^{66} - 15385 q^{67} - 344896 q^{68} - 88962 q^{69} - 14972 q^{70} + 114832 q^{71} - 547284 q^{72} + 32349 q^{73} - 294308 q^{74} + 51636 q^{75} + 174924 q^{76} + 61789 q^{77} + 1263536 q^{78} - 72595 q^{79} + 1108900 q^{80} - 48060 q^{81} + 186420 q^{82} - 557528 q^{83} - 190900 q^{84} - 262790 q^{85} - 940948 q^{86} - 313350 q^{87} - 1180668 q^{88} - 184539 q^{89} - 653628 q^{90} + 722562 q^{91} - 26020 q^{92} + 692669 q^{93} + 139964 q^{94} + 893683 q^{95} + 1789724 q^{96} + 368106 q^{97} + 1446012 q^{98} - 1284092 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.6.a \(\chi_{112}(1, \cdot)\) 112.6.a.a 1 1
112.6.a.b 1
112.6.a.c 1
112.6.a.d 1
112.6.a.e 1
112.6.a.f 1
112.6.a.g 1
112.6.a.h 2
112.6.a.i 2
112.6.a.j 2
112.6.a.k 2
112.6.b \(\chi_{112}(57, \cdot)\) None 0 1
112.6.e \(\chi_{112}(55, \cdot)\) None 0 1
112.6.f \(\chi_{112}(111, \cdot)\) 112.6.f.a 8 1
112.6.f.b 12
112.6.i \(\chi_{112}(65, \cdot)\) 112.6.i.a 2 2
112.6.i.b 4
112.6.i.c 4
112.6.i.d 4
112.6.i.e 4
112.6.i.f 10
112.6.i.g 10
112.6.j \(\chi_{112}(27, \cdot)\) n/a 156 2
112.6.m \(\chi_{112}(29, \cdot)\) n/a 120 2
112.6.p \(\chi_{112}(31, \cdot)\) 112.6.p.a 12 2
112.6.p.b 14
112.6.p.c 14
112.6.q \(\chi_{112}(87, \cdot)\) None 0 2
112.6.t \(\chi_{112}(9, \cdot)\) None 0 2
112.6.v \(\chi_{112}(3, \cdot)\) n/a 312 4
112.6.w \(\chi_{112}(37, \cdot)\) n/a 312 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(112)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 1}\)