↑

Properties

Label 112.4
Level 112
Weight 4
Dimension 599
Nonzero newspaces 8
Newform subspaces 29
Sturm bound 3072
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 29 \)
Sturm bound: \(3072\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(112))\).

Total New Old
Modular forms 1236 643 593
Cusp forms 1068 599 469
Eisenstein series 168 44 124

Trace form

\( 599 q - 8 q^{2} - 13 q^{3} - 28 q^{4} - 7 q^{5} + 52 q^{6} + 15 q^{7} + 64 q^{8} + 19 q^{9} + O(q^{10}) \) \( 599 q - 8 q^{2} - 13 q^{3} - 28 q^{4} - 7 q^{5} + 52 q^{6} + 15 q^{7} + 64 q^{8} + 19 q^{9} + 124 q^{10} - 133 q^{11} - 212 q^{12} - 58 q^{13} - 200 q^{14} + 246 q^{15} - 572 q^{16} - 119 q^{17} - 360 q^{18} - 139 q^{19} + 380 q^{20} - 151 q^{21} + 1152 q^{22} + 5 q^{23} + 1684 q^{24} + 743 q^{25} + 516 q^{26} + 578 q^{27} - 292 q^{28} + 278 q^{29} - 2484 q^{30} - 705 q^{31} - 1948 q^{32} - 443 q^{33} - 884 q^{34} - 1055 q^{35} + 1168 q^{36} - 427 q^{37} + 2452 q^{38} - 734 q^{39} + 2660 q^{40} + 390 q^{41} + 3260 q^{42} + 2368 q^{43} + 1948 q^{44} + 2112 q^{45} - 176 q^{46} + 3241 q^{47} - 3428 q^{48} - 4065 q^{49} - 3576 q^{50} + 1541 q^{51} - 4184 q^{52} - 1127 q^{53} - 6164 q^{54} - 1138 q^{55} - 4144 q^{56} - 4742 q^{57} - 4144 q^{58} - 5789 q^{59} - 5508 q^{60} - 4135 q^{61} - 1256 q^{62} - 2871 q^{63} + 380 q^{64} + 2350 q^{65} + 7444 q^{66} - 3265 q^{67} + 7808 q^{68} + 1422 q^{69} + 7268 q^{70} - 80 q^{71} + 3948 q^{72} - 959 q^{73} + 892 q^{74} + 7836 q^{75} + 2444 q^{76} + 3277 q^{77} + 1520 q^{78} + 10157 q^{79} + 5284 q^{80} + 3246 q^{81} + 1396 q^{82} + 10072 q^{83} - 1972 q^{84} + 4082 q^{85} - 7540 q^{86} + 2322 q^{87} - 3068 q^{88} + 1113 q^{89} - 6396 q^{90} + 3466 q^{91} - 4516 q^{92} + 5525 q^{93} - 7556 q^{94} - 2141 q^{95} - 6628 q^{96} - 1442 q^{97} - 5604 q^{98} - 7868 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.4.a \(\chi_{112}(1, \cdot)\) 112.4.a.a 1 1
112.4.a.b 1
112.4.a.c 1
112.4.a.d 1
112.4.a.e 1
112.4.a.f 1
112.4.a.g 1
112.4.a.h 2
112.4.b \(\chi_{112}(57, \cdot)\) None 0 1
112.4.e \(\chi_{112}(55, \cdot)\) None 0 1
112.4.f \(\chi_{112}(111, \cdot)\) 112.4.f.a 4 1
112.4.f.b 8
112.4.i \(\chi_{112}(65, \cdot)\) 112.4.i.a 2 2
112.4.i.b 2
112.4.i.c 2
112.4.i.d 4
112.4.i.e 6
112.4.i.f 6
112.4.j \(\chi_{112}(27, \cdot)\) 112.4.j.a 4 2
112.4.j.b 88
112.4.m \(\chi_{112}(29, \cdot)\) 112.4.m.a 34 2
112.4.m.b 38
112.4.p \(\chi_{112}(31, \cdot)\) 112.4.p.a 2 2
112.4.p.b 2
112.4.p.c 2
112.4.p.d 2
112.4.p.e 4
112.4.p.f 6
112.4.p.g 6
112.4.q \(\chi_{112}(87, \cdot)\) None 0 2
112.4.t \(\chi_{112}(9, \cdot)\) None 0 2
112.4.v \(\chi_{112}(3, \cdot)\) 112.4.v.a 184 4
112.4.w \(\chi_{112}(37, \cdot)\) 112.4.w.a 184 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

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