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Properties

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

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Defining parameters

Level: \( N \) = \( 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 8 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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