Properties

Label 690.2.n
Level $690$
Weight $2$
Character orbit 690.n
Rep. character $\chi_{690}(89,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $480$
Newform subspaces $2$
Sturm bound $288$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.n (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 345 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(17\)

Dimensions

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

Total New Old
Modular forms 1520 480 1040
Cusp forms 1360 480 880
Eisenstein series 160 0 160

Trace form

\( 480q - 48q^{4} + 4q^{6} - 12q^{9} + O(q^{10}) \) \( 480q - 48q^{4} + 4q^{6} - 12q^{9} + 22q^{15} - 48q^{16} + 4q^{24} - 24q^{25} + 44q^{30} + 56q^{31} - 12q^{36} - 8q^{46} + 140q^{49} - 18q^{54} - 52q^{55} - 22q^{60} + 88q^{61} - 48q^{64} + 88q^{66} - 204q^{69} - 72q^{70} - 184q^{75} - 88q^{79} + 148q^{81} - 22q^{84} + 44q^{85} + 32q^{94} + 4q^{96} + O(q^{100}) \)

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.n.a \(240\) \(5.510\) None \(-24\) \(2\) \(0\) \(0\)
690.2.n.b \(240\) \(5.510\) None \(24\) \(-2\) \(0\) \(0\)

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

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