Properties

Label 684.3.e
Level $684$
Weight $3$
Character orbit 684.e
Rep. character $\chi_{684}(305,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $360$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(360\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(684, [\chi])\).

Total New Old
Modular forms 252 12 240
Cusp forms 228 12 216
Eisenstein series 24 0 24

Trace form

\( 12 q + 16 q^{7} + O(q^{10}) \) \( 12 q + 16 q^{7} - 16 q^{13} - 12 q^{25} - 40 q^{31} - 32 q^{37} + 92 q^{43} - 84 q^{55} - 48 q^{61} - 88 q^{67} + 148 q^{73} - 56 q^{79} + 228 q^{85} - 8 q^{91} + 72 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
684.3.e.a $12$ $18.638$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(16\) \(q+\beta _{1}q^{5}+(1+\beta _{4})q^{7}-\beta _{10}q^{11}+(-1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)