Properties

Label 690.2.x
Level $690$
Weight $2$
Character orbit 690.x
Rep. character $\chi_{690}(77,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $960$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.x (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 345 \)
Character field: \(\Q(\zeta_{44})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(690, [\chi])\).

Total New Old
Modular forms 3040 960 2080
Cusp forms 2720 960 1760
Eisenstein series 320 0 320

Trace form

\( 960q + 8q^{3} + 8q^{6} + O(q^{10}) \) \( 960q + 8q^{3} + 8q^{6} - 8q^{12} - 16q^{13} + 8q^{15} + 96q^{16} + 72q^{18} + 16q^{22} + 32q^{25} + 8q^{27} - 16q^{31} + 36q^{33} - 8q^{36} + 24q^{37} - 48q^{43} - 16q^{46} - 8q^{48} - 32q^{51} + 16q^{52} - 64q^{55} - 16q^{57} + 8q^{60} - 96q^{61} + 72q^{63} - 144q^{66} + 64q^{67} - 16q^{70} + 16q^{72} + 48q^{73} + 4q^{75} - 24q^{78} - 248q^{81} - 32q^{82} + 64q^{85} - 8q^{87} + 16q^{88} + 40q^{90} - 96q^{91} - 104q^{93} - 8q^{96} - 264q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(690, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
690.2.x.a \(960\) \(5.510\) None \(0\) \(8\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(690, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)