Properties

Label 162.4.g
Level 162
Weight 4
Character orbit g
Rep. character \(\chi_{162}(7,\cdot)\)
Character field \(\Q(\zeta_{27})\)
Dimension 486
Newform subspaces 2
Sturm bound 108
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 162.g (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
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 1494 486 1008
Cusp forms 1422 486 936
Eisenstein series 72 0 72

Trace form

\( 486q + O(q^{10}) \) \( 486q - 414q^{18} - 288q^{20} - 216q^{21} + 756q^{23} + 1404q^{26} + 1404q^{27} + 1080q^{29} + 756q^{30} - 864q^{33} - 2484q^{35} - 1152q^{36} - 954q^{38} - 1854q^{41} - 1026q^{45} + 594q^{47} + 2961q^{51} + 2862q^{53} + 2214q^{57} + 1449q^{59} - 1998q^{63} + 7254q^{65} + 9360q^{66} - 5508q^{67} + 1368q^{68} + 4122q^{69} - 1620q^{70} + 1440q^{71} - 576q^{72} - 5472q^{74} - 9000q^{75} + 1620q^{76} - 19584q^{77} - 10656q^{78} + 8424q^{79} - 2880q^{80} - 11520q^{81} - 10656q^{83} - 2448q^{84} + 6480q^{85} - 7200q^{86} - 10944q^{87} + 648q^{88} - 3555q^{89} + 1440q^{90} + 3744q^{92} + 9090q^{93} - 5508q^{94} + 16074q^{95} + 2880q^{96} - 10368q^{97} + 16272q^{98} + 20754q^{99} + O(q^{100}) \)

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.g.a \(234\) \(9.558\) None \(0\) \(0\) \(0\) \(0\)
162.4.g.b \(252\) \(9.558\) None \(0\) \(0\) \(0\) \(0\)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database