Properties

Label 69.2.g
Level $69$
Weight $2$
Character orbit 69.g
Rep. character $\chi_{69}(5,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $60$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 69.g (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(69, [\chi])\).

Total New Old
Modular forms 100 100 0
Cusp forms 60 60 0
Eisenstein series 40 40 0

Trace form

\( 60q - 11q^{3} - 10q^{4} - 14q^{6} - 22q^{7} - 11q^{9} + O(q^{10}) \) \( 60q - 11q^{3} - 10q^{4} - 14q^{6} - 22q^{7} - 11q^{9} - 22q^{10} + 4q^{12} - 22q^{13} - 46q^{16} + 12q^{18} - 22q^{19} + 22q^{21} + 50q^{24} + 8q^{25} + 10q^{27} - 22q^{28} + 33q^{30} - 22q^{31} + 22q^{36} + 22q^{37} + 13q^{39} + 132q^{40} - 11q^{42} + 22q^{43} + 66q^{46} - 58q^{48} + 68q^{49} - 11q^{51} + 94q^{52} - 33q^{54} - 44q^{57} - 8q^{58} - 121q^{60} - 66q^{61} - 66q^{63} - 20q^{64} - 66q^{66} - 44q^{67} - 66q^{69} - 132q^{70} - 101q^{72} - 44q^{73} - 44q^{75} - 110q^{76} + 84q^{78} - 66q^{79} + 77q^{81} - 132q^{82} + 77q^{84} - 44q^{85} + 73q^{87} + 66q^{88} + 176q^{90} + 116q^{93} + 100q^{94} + 85q^{96} + 44q^{97} + 121q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(69, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
69.2.g.a \(60\) \(0.551\) None \(0\) \(-11\) \(0\) \(-22\)