Properties

Label 690.2.r
Level $690$
Weight $2$
Character orbit 690.r
Rep. character $\chi_{690}(49,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $240$
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.r (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 1520 240 1280
Cusp forms 1360 240 1120
Eisenstein series 160 0 160

Trace form

\( 240q + 24q^{4} + 8q^{5} + 24q^{9} + O(q^{10}) \) \( 240q + 24q^{4} + 8q^{5} + 24q^{9} - 8q^{11} - 8q^{14} - 8q^{15} - 24q^{16} + 16q^{19} + 36q^{20} - 8q^{21} + 80q^{25} + 8q^{26} + 24q^{29} + 8q^{30} + 16q^{31} + 8q^{34} - 32q^{35} - 24q^{36} + 36q^{39} + 16q^{41} + 8q^{44} - 8q^{45} + 8q^{49} - 8q^{50} + 8q^{51} + 36q^{55} + 8q^{56} + 44q^{59} + 8q^{60} - 96q^{61} + 24q^{64} + 8q^{65} - 8q^{66} + 112q^{70} + 8q^{71} - 8q^{74} - 16q^{76} + 112q^{79} + 8q^{80} - 24q^{81} + 8q^{84} - 8q^{85} - 48q^{86} - 56q^{89} + 144q^{91} - 92q^{95} - 80q^{99} + O(q^{100}) \)

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.r.a \(120\) \(5.510\) None \(0\) \(0\) \(0\) \(0\)
690.2.r.b \(120\) \(5.510\) None \(0\) \(0\) \(8\) \(0\)

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

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