Properties

Label 2808.1.bs
Level $2808$
Weight $1$
Character orbit 2808.bs
Rep. character $\chi_{2808}(883,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $2$
Sturm bound $504$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 2808 = 2^{3} \cdot 3^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2808.bs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 936 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(504\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2808, [\chi])\).

Total New Old
Modular forms 60 20 40
Cusp forms 36 12 24
Eisenstein series 24 8 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12q - 6q^{4} + O(q^{10}) \) \( 12q - 6q^{4} - 6q^{16} - 6q^{25} - 12q^{26} + 12q^{35} - 6q^{49} + 12q^{62} + 12q^{64} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2808, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2808.1.bs.a \(6\) \(1.401\) \(\Q(\zeta_{18})\) \(D_{9}\) \(\Q(\sqrt{-26}) \) None \(-3\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
2808.1.bs.b \(6\) \(1.401\) \(\Q(\zeta_{18})\) \(D_{9}\) \(\Q(\sqrt{-26}) \) None \(3\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(\zeta_{18}^{5}+\zeta_{18}^{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2808, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2808, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 2}\)