Properties

Label 690.2.h
Level $690$
Weight $2$
Character orbit 690.h
Rep. character $\chi_{690}(689,\cdot)$
Character field $\Q$
Dimension $48$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 345 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(47\)

Dimensions

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

Total New Old
Modular forms 152 48 104
Cusp forms 136 48 88
Eisenstein series 16 0 16

Trace form

\( 48q + 48q^{4} - 4q^{6} + 12q^{9} + O(q^{10}) \) \( 48q + 48q^{4} - 4q^{6} + 12q^{9} + 48q^{16} - 4q^{24} + 24q^{25} - 56q^{31} + 12q^{36} + 8q^{46} - 8q^{49} - 4q^{54} + 8q^{55} + 48q^{64} - 16q^{69} - 16q^{70} + 8q^{75} + 28q^{81} - 88q^{85} - 32q^{94} - 4q^{96} + O(q^{100}) \)

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

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

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