Properties

Label 819.1.ef
Level $819$
Weight $1$
Character orbit 819.ef
Rep. character $\chi_{819}(451,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 819.ef (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(819, [\chi])\).

Total New Old
Modular forms 18 6 12
Cusp forms 2 2 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 2 0 0 0

Trace form

\( 2q - 2q^{4} + q^{7} + O(q^{10}) \) \( 2q - 2q^{4} + q^{7} - q^{13} + 2q^{16} + 3q^{19} - q^{25} - q^{28} + 2q^{37} - q^{43} - q^{49} + q^{52} + 3q^{61} - 2q^{64} - 2q^{67} - 3q^{73} - 3q^{76} - 2q^{79} - 2q^{91} + 3q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
819.1.ef.a \(2\) \(0.409\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{13}+q^{16}+(1+\cdots)q^{19}+\cdots\)