Properties

Label 690.2.e
Level $690$
Weight $2$
Character orbit 690.e
Rep. character $\chi_{690}(551,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $2$
Sturm bound $288$
Trace bound $5$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
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 152 32 120
Cusp forms 136 32 104
Eisenstein series 16 0 16

Trace form

\( 32q - 32q^{4} + 4q^{6} + 4q^{9} + O(q^{10}) \) \( 32q - 32q^{4} + 4q^{6} + 4q^{9} + 32q^{16} + 16q^{18} - 4q^{24} + 32q^{25} + 48q^{27} + 8q^{31} - 4q^{36} - 16q^{39} - 8q^{46} - 8q^{49} - 52q^{54} + 24q^{55} - 16q^{58} - 32q^{64} + 8q^{69} + 24q^{70} - 16q^{72} - 32q^{73} - 24q^{78} + 44q^{81} - 32q^{82} + 40q^{87} - 8q^{93} - 48q^{94} + 4q^{96} + O(q^{100}) \)

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.e.a \(16\) \(5.510\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-16\) \(0\) \(q+\beta _{9}q^{2}+\beta _{2}q^{3}-q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
690.2.e.b \(16\) \(5.510\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(16\) \(0\) \(q+\beta _{9}q^{2}+\beta _{2}q^{3}-q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

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

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