Properties

Label 690.2.q
Level $690$
Weight $2$
Character orbit 690.q
Rep. character $\chi_{690}(11,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $320$
Newform subspaces $2$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.q (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

Total New Old
Modular forms 1520 320 1200
Cusp forms 1360 320 1040
Eisenstein series 160 0 160

Trace form

\( 320q + 32q^{4} - 4q^{6} - 4q^{9} + O(q^{10}) \) \( 320q + 32q^{4} - 4q^{6} - 4q^{9} - 32q^{16} - 16q^{18} + 132q^{21} + 4q^{24} - 32q^{25} + 84q^{27} - 8q^{31} + 4q^{36} + 16q^{39} + 88q^{43} + 8q^{46} + 140q^{49} + 30q^{54} + 20q^{55} - 132q^{57} - 72q^{58} - 88q^{61} - 220q^{63} + 32q^{64} - 88q^{66} - 88q^{67} - 8q^{69} - 24q^{70} - 72q^{72} - 56q^{73} - 108q^{78} - 88q^{79} - 132q^{81} - 56q^{82} - 22q^{84} + 92q^{87} + 8q^{93} + 48q^{94} - 4q^{96} + 132q^{99} + O(q^{100}) \)

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.q.a \(160\) \(5.510\) None \(0\) \(0\) \(-16\) \(0\)
690.2.q.b \(160\) \(5.510\) None \(0\) \(0\) \(16\) \(0\)

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

\( S_{2}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)