Properties

Label 69.2
Level 69
Weight 2
Dimension 109
Nonzero newspaces 4
Newforms 7
Sturm bound 704
Trace bound 1

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Defining parameters

Level: \( N \) = \( 69 = 3 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 7 \)
Sturm bound: \(704\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(69))\).

Total New Old
Modular forms 220 153 67
Cusp forms 133 109 24
Eisenstein series 87 44 43

Trace form

\( 109q - 3q^{2} - 12q^{3} - 29q^{4} - 6q^{5} - 14q^{6} - 30q^{7} - 15q^{8} - 12q^{9} + O(q^{10}) \) \( 109q - 3q^{2} - 12q^{3} - 29q^{4} - 6q^{5} - 14q^{6} - 30q^{7} - 15q^{8} - 12q^{9} - 40q^{10} - 12q^{11} - 18q^{12} - 36q^{13} - 24q^{14} - 6q^{15} - 9q^{16} + 4q^{17} + 30q^{18} - 20q^{19} + 46q^{20} + 14q^{21} + 8q^{22} + 21q^{23} + 29q^{24} - 9q^{25} + 2q^{26} + 21q^{27} + 10q^{28} - 8q^{29} + 15q^{30} - 32q^{31} - 19q^{32} - 12q^{33} - 32q^{34} - 4q^{35} + 4q^{36} + 28q^{37} + 50q^{38} + 19q^{39} + 64q^{40} + 2q^{41} + 75q^{42} + 22q^{43} + 70q^{44} - 6q^{45} + 85q^{46} + 40q^{47} + 68q^{48} + 53q^{49} + 61q^{50} + 15q^{51} + 100q^{52} - 10q^{53} - 14q^{54} - 6q^{55} - 10q^{56} - 20q^{57} - 2q^{58} - 16q^{59} - 141q^{60} - 84q^{61} - 96q^{62} - 74q^{63} - 149q^{64} - 84q^{65} - 102q^{66} - 90q^{67} - 126q^{68} - 89q^{69} - 188q^{70} - 72q^{71} - 158q^{72} - 96q^{73} - 92q^{74} - 75q^{75} - 52q^{76} - 8q^{77} - 9q^{78} - 14q^{79} + 12q^{80} + 76q^{81} - 16q^{82} + 4q^{83} + 21q^{84} + 90q^{85} + 88q^{86} + 91q^{87} + 62q^{88} + 42q^{89} + 158q^{90} + 64q^{91} + 37q^{92} + 78q^{93} + 76q^{94} + 78q^{95} + 135q^{96} + 78q^{97} + 93q^{98} + 131q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)

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
69.2.a \(\chi_{69}(1, \cdot)\) 69.2.a.a 1 1
69.2.a.b 2
69.2.c \(\chi_{69}(68, \cdot)\) 69.2.c.a 6 1
69.2.e \(\chi_{69}(4, \cdot)\) 69.2.e.a 10 10
69.2.e.b 10
69.2.e.c 20
69.2.g \(\chi_{69}(5, \cdot)\) 69.2.g.a 60 10

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(69))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(69)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)