Properties

Label 118.2
Level 118
Weight 2
Dimension 144
Nonzero newspaces 2
Newforms 6
Sturm bound 1740
Trace bound 1

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Defining parameters

Level: \( N \) = \( 118 = 2 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 6 \)
Sturm bound: \(1740\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(118))\).

Total New Old
Modular forms 493 144 349
Cusp forms 378 144 234
Eisenstein series 115 0 115

Trace form

\(144q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut -\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(144q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut -\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut -\mathstrut 24q^{15} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut -\mathstrut 13q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut -\mathstrut 4q^{24} \) \(\mathstrut -\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 14q^{26} \) \(\mathstrut -\mathstrut 40q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 30q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 32q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut -\mathstrut 48q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 48q^{35} \) \(\mathstrut -\mathstrut 13q^{36} \) \(\mathstrut -\mathstrut 38q^{37} \) \(\mathstrut -\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 56q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut -\mathstrut 20q^{45} \) \(\mathstrut +\mathstrut 34q^{46} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 85q^{50} \) \(\mathstrut +\mathstrut 160q^{51} \) \(\mathstrut +\mathstrut 44q^{52} \) \(\mathstrut +\mathstrut 62q^{53} \) \(\mathstrut +\mathstrut 163q^{54} \) \(\mathstrut +\mathstrut 102q^{55} \) \(\mathstrut -\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 210q^{57} \) \(\mathstrut +\mathstrut 28q^{58} \) \(\mathstrut +\mathstrut 57q^{59} \) \(\mathstrut +\mathstrut 150q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut +\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 186q^{63} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut +\mathstrut 90q^{65} \) \(\mathstrut +\mathstrut 155q^{66} \) \(\mathstrut +\mathstrut 48q^{67} \) \(\mathstrut +\mathstrut 40q^{68} \) \(\mathstrut +\mathstrut 136q^{69} \) \(\mathstrut +\mathstrut 68q^{70} \) \(\mathstrut +\mathstrut 44q^{71} \) \(\mathstrut -\mathstrut 13q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 20q^{74} \) \(\mathstrut -\mathstrut 66q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut -\mathstrut 56q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut -\mathstrut 121q^{81} \) \(\mathstrut -\mathstrut 42q^{82} \) \(\mathstrut -\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 108q^{85} \) \(\mathstrut -\mathstrut 44q^{86} \) \(\mathstrut -\mathstrut 120q^{87} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 90q^{89} \) \(\mathstrut -\mathstrut 78q^{90} \) \(\mathstrut -\mathstrut 112q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 128q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 120q^{95} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut -\mathstrut 57q^{98} \) \(\mathstrut -\mathstrut 69q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)

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
118.2.a \(\chi_{118}(1, \cdot)\) 118.2.a.a 1 1
118.2.a.b 1
118.2.a.c 1
118.2.a.d 1
118.2.c \(\chi_{118}(3, \cdot)\) 118.2.c.a 56 28
118.2.c.b 84

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(118))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(118)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)