Properties

Label 684.1.q
Level $684$
Weight $1$
Character orbit 684.q
Rep. character $\chi_{684}(163,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 684.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(684, [\chi])\).

Total New Old
Modular forms 24 12 12
Cusp forms 8 8 0
Eisenstein series 16 4 12

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 8 0

Trace form

\( 8q + O(q^{10}) \) \( 8q + 4q^{10} + 4q^{13} + 4q^{16} + 4q^{22} - 4q^{25} + 4q^{28} - 8q^{37} - 4q^{40} - 8q^{46} - 4q^{61} - 4q^{70} - 4q^{73} - 4q^{76} - 8q^{88} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
684.1.q.a \(8\) \(0.341\) \(\Q(\zeta_{24})\) \(S_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{11}+\cdots)q^{5}+\cdots\)