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Properties

Label 162.4.e
Level $162$
Weight $4$
Character orbit 162.e
Rep. character $\chi_{162}(19,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $54$
Newform subspaces $2$
Sturm bound $108$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
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: \(108\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(162, [\chi])\).

Total New Old
Modular forms 522 54 468
Cusp forms 450 54 396
Eisenstein series 72 0 72

Trace form

\( 54 q + 24 q^{5} - 24 q^{8} + O(q^{10}) \) \( 54 q + 24 q^{5} - 24 q^{8} + 51 q^{11} + 132 q^{14} - 204 q^{17} - 192 q^{20} + 54 q^{22} + 660 q^{23} + 432 q^{25} + 936 q^{26} + 762 q^{29} + 108 q^{31} - 270 q^{34} - 1248 q^{35} - 672 q^{38} - 2019 q^{41} - 513 q^{43} - 264 q^{44} - 162 q^{47} + 594 q^{49} + 792 q^{50} + 3588 q^{53} + 528 q^{56} + 462 q^{59} - 54 q^{61} - 1488 q^{62} - 1728 q^{64} - 9384 q^{65} + 2511 q^{67} - 1032 q^{68} + 1080 q^{70} - 240 q^{71} + 432 q^{73} + 3084 q^{74} - 1080 q^{76} + 10308 q^{77} - 5616 q^{79} + 960 q^{80} + 4698 q^{83} - 4320 q^{85} + 3618 q^{86} - 432 q^{88} - 3669 q^{89} - 540 q^{91} - 2256 q^{92} + 3672 q^{94} - 13902 q^{95} + 6885 q^{97} - 5358 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.4.e.a 162.e 27.e $24$ $9.558$ None \(0\) \(0\) \(12\) \(-33\) $\mathrm{SU}(2)[C_{9}]$
162.4.e.b 162.e 27.e $30$ $9.558$ None \(0\) \(0\) \(12\) \(33\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{4}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

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