Properties

Label 690.2.j
Level $690$
Weight $2$
Character orbit 690.j
Rep. character $\chi_{690}(367,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(i)\)
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 304 48 256
Cusp forms 272 48 224
Eisenstein series 32 0 32

Trace form

\( 48q + O(q^{10}) \) \( 48q + 16q^{13} - 48q^{16} + 8q^{23} - 32q^{25} - 16q^{26} + 32q^{31} - 16q^{35} + 48q^{36} + 32q^{47} + 16q^{50} + 16q^{52} - 32q^{55} - 64q^{62} + 48q^{71} - 64q^{73} + 32q^{75} + 16q^{77} + 16q^{78} - 48q^{81} + 48q^{82} - 48q^{85} + 32q^{87} + 8q^{92} + 48q^{93} + 48q^{95} - 32q^{98} + O(q^{100}) \)

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.j.a \(24\) \(5.510\) None \(0\) \(0\) \(0\) \(0\)
690.2.j.b \(24\) \(5.510\) None \(0\) \(0\) \(0\) \(0\)

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

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