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Properties

Label 162.3.f
Level $162$
Weight $3$
Character orbit 162.f
Rep. character $\chi_{162}(17,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $36$
Newform subspaces $1$
Sturm bound $81$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.f (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(81\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(162, [\chi])\).

Total New Old
Modular forms 360 36 324
Cusp forms 288 36 252
Eisenstein series 72 0 72

Trace form

\( 36 q - 18 q^{5} + O(q^{10}) \) \( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.3.f.a 162.f 27.f $36$ $4.414$ None \(0\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{3}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(162, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)