Properties

Label 819.1.ff
Level $819$
Weight $1$
Character orbit 819.ff
Rep. character $\chi_{819}(163,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $4$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 819.ff (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
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 36 12 24
Cusp forms 4 4 0
Eisenstein series 32 8 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q + 2q^{7} + O(q^{10}) \) \( 4q + 2q^{7} + 2q^{16} + 2q^{19} - 2q^{31} - 2q^{37} + 6q^{43} - 2q^{49} - 2q^{52} - 4q^{67} - 4q^{73} - 4q^{76} - 2q^{97} + O(q^{100}) \)

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.ff.a \(4\) \(0.409\) \(\Q(\zeta_{12})\) \(D_{12}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}q^{4}+\zeta_{12}^{2}q^{7}+\zeta_{12}q^{13}+\zeta_{12}^{2}q^{16}+\cdots\)