Properties

Label 114.2
Level 114
Weight 2
Dimension 91
Nonzero newspaces 6
Newforms 21
Sturm bound 1440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newforms: \( 21 \)
Sturm bound: \(1440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(114))\).

Total New Old
Modular forms 432 91 341
Cusp forms 289 91 198
Eisenstein series 143 0 143

Trace form

\(91q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(91q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 5q^{12} \) \(\mathstrut -\mathstrut 34q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 65q^{19} \) \(\mathstrut -\mathstrut 30q^{20} \) \(\mathstrut -\mathstrut 34q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut -\mathstrut 41q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut -\mathstrut 14q^{27} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut +\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 19q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 8q^{42} \) \(\mathstrut -\mathstrut 28q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut +\mathstrut 31q^{50} \) \(\mathstrut +\mathstrut 99q^{51} \) \(\mathstrut +\mathstrut 14q^{52} \) \(\mathstrut +\mathstrut 54q^{53} \) \(\mathstrut +\mathstrut 55q^{54} \) \(\mathstrut +\mathstrut 72q^{55} \) \(\mathstrut +\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 109q^{57} \) \(\mathstrut +\mathstrut 30q^{58} \) \(\mathstrut +\mathstrut 60q^{59} \) \(\mathstrut +\mathstrut 42q^{60} \) \(\mathstrut +\mathstrut 50q^{61} \) \(\mathstrut +\mathstrut 32q^{62} \) \(\mathstrut +\mathstrut 74q^{63} \) \(\mathstrut +\mathstrut q^{64} \) \(\mathstrut +\mathstrut 48q^{65} \) \(\mathstrut +\mathstrut 84q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 18q^{68} \) \(\mathstrut +\mathstrut 78q^{69} \) \(\mathstrut +\mathstrut 48q^{70} \) \(\mathstrut +\mathstrut 36q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 19q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 22q^{78} \) \(\mathstrut -\mathstrut 76q^{79} \) \(\mathstrut +\mathstrut 6q^{80} \) \(\mathstrut -\mathstrut 71q^{81} \) \(\mathstrut -\mathstrut 30q^{82} \) \(\mathstrut -\mathstrut 60q^{83} \) \(\mathstrut -\mathstrut 46q^{84} \) \(\mathstrut -\mathstrut 36q^{85} \) \(\mathstrut -\mathstrut 28q^{86} \) \(\mathstrut -\mathstrut 150q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 54q^{89} \) \(\mathstrut -\mathstrut 84q^{90} \) \(\mathstrut -\mathstrut 80q^{91} \) \(\mathstrut -\mathstrut 48q^{92} \) \(\mathstrut -\mathstrut 118q^{93} \) \(\mathstrut -\mathstrut 96q^{94} \) \(\mathstrut +\mathstrut 6q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 10q^{97} \) \(\mathstrut -\mathstrut 87q^{98} \) \(\mathstrut -\mathstrut 69q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)

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
114.2.a \(\chi_{114}(1, \cdot)\) 114.2.a.a 1 1
114.2.a.b 1
114.2.a.c 1
114.2.b \(\chi_{114}(113, \cdot)\) 114.2.b.a 2 1
114.2.b.b 2
114.2.b.c 2
114.2.b.d 2
114.2.e \(\chi_{114}(7, \cdot)\) 114.2.e.a 2 2
114.2.e.b 2
114.2.h \(\chi_{114}(65, \cdot)\) 114.2.h.a 2 2
114.2.h.b 2
114.2.h.c 2
114.2.h.d 2
114.2.h.e 4
114.2.h.f 4
114.2.i \(\chi_{114}(25, \cdot)\) 114.2.i.a 6 6
114.2.i.b 6
114.2.i.c 6
114.2.i.d 6
114.2.l \(\chi_{114}(29, \cdot)\) 114.2.l.a 18 6
114.2.l.b 18

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(114))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(114)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)