Properties

Label 819.2.cf
Level $819$
Weight $2$
Character orbit 819.cf
Rep. character $\chi_{819}(647,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.cf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(819, [\chi])\).

Total New Old
Modular forms 240 76 164
Cusp forms 208 76 132
Eisenstein series 32 0 32

Trace form

\( 76 q - 40 q^{4} + 2 q^{7} + O(q^{10}) \) \( 76 q - 40 q^{4} + 2 q^{7} - 20 q^{13} - 44 q^{16} - 28 q^{19} + 12 q^{22} + 42 q^{25} - 28 q^{28} + 10 q^{31} + 30 q^{37} - 60 q^{40} - 16 q^{43} + 36 q^{46} - 34 q^{49} + 28 q^{52} + 24 q^{55} + 104 q^{64} - 60 q^{70} - 44 q^{73} + 56 q^{76} + 30 q^{79} + 48 q^{85} - 96 q^{88} + 2 q^{91} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
819.2.cf.a 819.cf 273.y $76$ $6.540$ None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(819, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)