Properties

Label 690.2.w
Level $690$
Weight $2$
Character orbit 690.w
Rep. character $\chi_{690}(7,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $480$
Newform subspaces $2$
Sturm bound $288$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.w (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 3040 480 2560
Cusp forms 2720 480 2240
Eisenstein series 320 0 320

Trace form

\( 480q + O(q^{10}) \) \( 480q - 16q^{13} + 48q^{16} + 168q^{23} + 32q^{25} + 16q^{26} + 88q^{28} - 32q^{31} + 16q^{35} - 48q^{36} + 88q^{37} + 144q^{47} - 16q^{50} - 16q^{52} + 32q^{55} + 88q^{57} + 176q^{61} + 64q^{62} - 48q^{71} + 64q^{73} - 32q^{75} - 16q^{77} - 16q^{78} + 48q^{81} - 48q^{82} + 136q^{85} - 32q^{87} - 8q^{92} - 48q^{93} + 40q^{95} - 144q^{98} + O(q^{100}) \)

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.w.a \(240\) \(5.510\) None \(0\) \(0\) \(0\) \(0\)
690.2.w.b \(240\) \(5.510\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)