Properties

Label 819.2.gh
Level $819$
Weight $2$
Character orbit 819.gh
Rep. character $\chi_{819}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $180$
Newform subspaces $5$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.gh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 480 196 284
Cusp forms 416 180 236
Eisenstein series 64 16 48

Trace form

\( 180 q + 2 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} + 4 q^{8} + O(q^{10}) \) \( 180 q + 2 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 12 q^{10} - 10 q^{11} - 4 q^{14} + 86 q^{16} + 6 q^{17} + 20 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 36 q^{26} - 50 q^{28} - 8 q^{29} - 22 q^{31} + 12 q^{34} - 14 q^{35} - 8 q^{37} - 72 q^{40} + 18 q^{41} - 24 q^{43} + 70 q^{44} + 10 q^{46} + 42 q^{47} - 20 q^{49} + 30 q^{50} - 44 q^{52} + 4 q^{53} + 42 q^{55} - 12 q^{56} - 18 q^{58} + 6 q^{59} - 36 q^{62} - 54 q^{65} + 42 q^{68} - 100 q^{70} + 6 q^{71} + 10 q^{73} + 46 q^{74} - 100 q^{76} + 20 q^{79} - 108 q^{80} + 84 q^{82} + 18 q^{83} - 14 q^{85} + 78 q^{86} - 18 q^{89} + 90 q^{91} + 20 q^{92} - 42 q^{95} + 10 q^{97} - 40 q^{98} + O(q^{100}) \)

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.gh.a 819.gh 91.w $4$ $6.540$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{12}]$ \(q+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+(-\zeta_{12}+3\zeta_{12}^{3})q^{7}+\cdots\)
819.2.gh.b 819.gh 91.w $28$ $6.540$ None \(2\) \(0\) \(6\) \(2\) $\mathrm{SU}(2)[C_{12}]$
819.2.gh.c 819.gh 91.w $36$ $6.540$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{12}]$
819.2.gh.d 819.gh 91.w $40$ $6.540$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$
819.2.gh.e 819.gh 91.w $72$ $6.540$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)