Properties

Label 67.2
Level 67
Weight 2
Dimension 155
Nonzero newspaces 4
Newforms 8
Sturm bound 748
Trace bound 1

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Defining parameters

Level: \( N \) = \( 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 8 \)
Sturm bound: \(748\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(67))\).

Total New Old
Modular forms 220 220 0
Cusp forms 155 155 0
Eisenstein series 65 65 0

Trace form

\( 155q - 30q^{2} - 29q^{3} - 26q^{4} - 27q^{5} - 21q^{6} - 25q^{7} - 18q^{8} - 20q^{9} + O(q^{10}) \) \( 155q - 30q^{2} - 29q^{3} - 26q^{4} - 27q^{5} - 21q^{6} - 25q^{7} - 18q^{8} - 20q^{9} - 15q^{10} - 21q^{11} - 5q^{12} - 19q^{13} - 9q^{14} - 9q^{15} - 2q^{16} - 15q^{17} + 6q^{18} - 13q^{19} + 9q^{20} - q^{21} + 3q^{22} - 9q^{23} + 27q^{24} - 2q^{25} + 9q^{26} + 7q^{27} + 23q^{28} - 3q^{29} + 39q^{30} - q^{31} + 30q^{32} + 15q^{33} + 21q^{34} + 15q^{35} + 58q^{36} + 5q^{37} + 27q^{38} + 23q^{39} + 57q^{40} + 9q^{41} + 63q^{42} + 11q^{43} + 51q^{44} + 45q^{45} + 39q^{46} + 15q^{47} + 91q^{48} + 24q^{49} + 60q^{50} + 39q^{51} + 21q^{52} - 12q^{53} - 12q^{54} - 60q^{55} - 111q^{56} - 30q^{57} - 75q^{58} - 39q^{59} - 129q^{60} - 103q^{61} - 3q^{62} - 72q^{63} - 236q^{64} - 81q^{65} - 186q^{66} - 32q^{67} - 72q^{68} - 3q^{69} - 153q^{70} - 93q^{71} - 168q^{72} - 102q^{73} + 15q^{74} - 41q^{75} - 157q^{76} - 3q^{77} + 3q^{78} - 30q^{79} - 45q^{80} - 11q^{81} - 6q^{82} + 18q^{83} + 147q^{84} + 75q^{85} + 99q^{86} + 87q^{87} + 147q^{88} + 57q^{89} + 201q^{90} + 79q^{91} + 135q^{92} + 95q^{93} + 111q^{94} + 87q^{95} + 219q^{96} + 65q^{97} + 138q^{98} + 123q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)

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
67.2.a \(\chi_{67}(1, \cdot)\) 67.2.a.a 1 1
67.2.a.b 2
67.2.a.c 2
67.2.c \(\chi_{67}(29, \cdot)\) 67.2.c.a 10 2
67.2.e \(\chi_{67}(9, \cdot)\) 67.2.e.a 10 10
67.2.e.b 10
67.2.e.c 20
67.2.g \(\chi_{67}(4, \cdot)\) 67.2.g.a 100 20