Properties

Label 819.2.fw
Level $819$
Weight $2$
Character orbit 819.fw
Rep. character $\chi_{819}(71,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $112$
Newform subspaces $2$
Sturm bound $224$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 480 112 368
Cusp forms 416 112 304
Eisenstein series 64 0 64

Trace form

\( 112 q + O(q^{10}) \) \( 112 q + 24 q^{10} + 40 q^{13} + 88 q^{16} + 16 q^{19} + 32 q^{22} - 32 q^{31} - 72 q^{34} - 24 q^{37} - 64 q^{40} - 144 q^{46} + 72 q^{58} + 24 q^{61} + 32 q^{67} - 96 q^{70} + 8 q^{73} - 32 q^{76} - 128 q^{79} - 240 q^{82} + 32 q^{85} - 144 q^{88} - 32 q^{91} - 24 q^{97} + O(q^{100}) \)

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.fw.a 819.fw 39.k $56$ $6.540$ None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{12}]$
819.2.fw.b 819.fw 39.k $56$ $6.540$ None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)