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Properties

Label 891.2.r
Level $891$
Weight $2$
Character orbit 891.r
Rep. character $\chi_{891}(34,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $1620$
Newform subspaces $2$
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.r (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Newform subspaces: \( 2 \)
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 1980 1620 360
Cusp forms 1908 1620 288
Eisenstein series 72 0 72

Trace form

\( 1620 q + O(q^{10}) \) \( 1620 q - 36 q^{20} - 54 q^{21} - 108 q^{24} - 108 q^{26} - 108 q^{30} - 108 q^{32} - 54 q^{35} - 36 q^{36} - 36 q^{41} - 90 q^{42} - 108 q^{47} - 234 q^{50} - 108 q^{53} - 108 q^{57} - 234 q^{60} - 108 q^{63} - 27 q^{67} - 90 q^{68} + 108 q^{69} - 108 q^{70} + 144 q^{71} + 432 q^{72} + 90 q^{75} + 144 q^{78} + 504 q^{80} + 144 q^{81} + 144 q^{83} + 504 q^{84} + 144 q^{86} + 90 q^{89} - 126 q^{90} + 342 q^{92} + 54 q^{93} - 108 q^{94} - 72 q^{95} - 27 q^{97} - 342 q^{98} + O(q^{100}) \)

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.r.a 891.r 81.g $774$ $7.115$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{27}]$
891.2.r.b 891.r 81.g $846$ $7.115$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{27}]$

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

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