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Properties

Label 891.2.j
Level $891$
Weight $2$
Character orbit 891.j
Rep. character $\chi_{891}(100,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $180$
Newform subspaces $3$
Sturm bound $216$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.j (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 3 \)
Sturm bound: \(216\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(891, [\chi])\).

Total New Old
Modular forms 684 180 504
Cusp forms 612 180 432
Eisenstein series 72 0 72

Trace form

\( 180 q + 3 q^{5} + O(q^{10}) \) \( 180 q + 3 q^{5} + 42 q^{14} + 18 q^{20} + 24 q^{23} - 9 q^{25} - 36 q^{26} + 36 q^{29} - 9 q^{31} - 12 q^{32} - 18 q^{35} + 30 q^{38} + 30 q^{44} - 30 q^{47} - 36 q^{49} - 132 q^{50} - 54 q^{52} - 72 q^{53} + 96 q^{56} - 54 q^{58} + 39 q^{59} - 36 q^{61} - 90 q^{64} + 114 q^{65} + 18 q^{67} + 12 q^{68} + 72 q^{70} + 60 q^{71} - 18 q^{73} + 162 q^{74} - 168 q^{80} + 12 q^{83} + 120 q^{86} + 57 q^{89} - 18 q^{91} - 204 q^{92} + 18 q^{94} - 132 q^{95} + 18 q^{97} - 114 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(891, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
891.2.j.a 891.j 27.e $6$ $7.115$ \(\Q(\zeta_{18})\) None \(3\) \(0\) \(9\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}^{2}+\zeta_{18}^{3})q^{2}+(-1+\zeta_{18}^{3}+\cdots)q^{4}+\cdots\)
891.2.j.b 891.j 27.e $72$ $7.115$ None \(-3\) \(0\) \(-12\) \(3\) $\mathrm{SU}(2)[C_{9}]$
891.2.j.c 891.j 27.e $102$ $7.115$ None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(891, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(891, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 2}\)