Properties

Label 162.4.e
Level 162
Weight 4
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
162.4.e.a \(24\) \(9.558\) None \(0\) \(0\) \(12\) \(-33\)
162.4.e.b \(30\) \(9.558\) None \(0\) \(0\) \(12\) \(33\)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database