Properties

Label 819.2.w
Level $819$
Weight $2$
Character orbit 819.w
Rep. character $\chi_{819}(8,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $2$
Sturm bound $224$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(i)\)
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 240 56 184
Cusp forms 208 56 152
Eisenstein series 32 0 32

Trace form

\( 56 q + O(q^{10}) \) \( 56 q + 8 q^{13} - 88 q^{16} - 16 q^{19} - 32 q^{22} + 32 q^{31} - 24 q^{34} + 24 q^{37} - 32 q^{40} + 48 q^{46} + 192 q^{55} + 120 q^{58} + 48 q^{61} - 80 q^{67} - 48 q^{70} - 8 q^{73} - 208 q^{76} + 32 q^{79} - 32 q^{85} - 16 q^{91} + 24 q^{97} + O(q^{100}) \)

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.w.a 819.w 39.f $28$ $6.540$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
819.2.w.b 819.w 39.f $28$ $6.540$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

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