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Properties

Label 162.2.e
Level $162$
Weight $2$
Character orbit 162.e
Rep. character $\chi_{162}(19,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $18$
Newform subspaces $2$
Sturm bound $54$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(54\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(162, [\chi])\).

Total New Old
Modular forms 198 18 180
Cusp forms 126 18 108
Eisenstein series 72 0 72

Trace form

\( 18 q + 6 q^{5} + 3 q^{8} + O(q^{10}) \) \( 18 q + 6 q^{5} + 3 q^{8} + 15 q^{11} + 6 q^{14} + 12 q^{17} - 12 q^{20} - 9 q^{22} - 24 q^{23} - 18 q^{25} - 36 q^{26} - 30 q^{29} - 18 q^{31} - 9 q^{34} - 6 q^{35} + 12 q^{38} + 15 q^{41} - 9 q^{43} + 6 q^{44} - 18 q^{49} + 36 q^{50} + 24 q^{53} + 6 q^{56} - 6 q^{59} - 18 q^{61} + 24 q^{62} - 9 q^{64} - 6 q^{65} + 27 q^{67} + 12 q^{68} + 36 q^{70} - 24 q^{71} - 18 q^{73} - 30 q^{74} + 18 q^{76} - 42 q^{77} + 72 q^{79} - 12 q^{80} + 72 q^{85} - 27 q^{86} + 18 q^{88} + 3 q^{89} - 18 q^{91} - 6 q^{92} + 36 q^{94} - 6 q^{95} + 27 q^{97} + 15 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.2.e.a 162.e 27.e $6$ $1.294$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
162.2.e.b 162.e 27.e $12$ $1.294$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{4}+\beta _{8})q^{2}-\beta _{6}q^{4}+(1-\beta _{2}+\beta _{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(162, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)