Properties

Label 162.2.g
Level $162$
Weight $2$
Character orbit 162.g
Rep. character $\chi_{162}(7,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $162$
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.g (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
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 522 162 360
Cusp forms 450 162 288
Eisenstein series 72 0 72

Trace form

\( 162q + O(q^{10}) \) \( 162q - 9q^{18} - 18q^{20} - 54q^{21} - 54q^{23} - 54q^{26} - 54q^{27} - 54q^{29} - 54q^{30} - 54q^{33} - 54q^{35} - 18q^{36} - 9q^{38} - 18q^{41} - 54q^{45} - 54q^{47} - 63q^{51} - 54q^{53} - 54q^{57} - 63q^{59} - 54q^{63} + 18q^{65} + 72q^{66} - 54q^{67} + 18q^{68} + 126q^{69} - 54q^{70} + 144q^{71} + 72q^{72} + 144q^{74} + 180q^{75} - 27q^{76} + 288q^{77} + 144q^{78} - 108q^{79} + 36q^{80} + 144q^{81} + 144q^{83} + 36q^{84} - 108q^{85} + 144q^{86} + 288q^{87} - 27q^{88} + 171q^{89} + 144q^{90} + 72q^{92} + 126q^{93} - 54q^{94} + 90q^{95} + 18q^{96} - 54q^{97} + 72q^{98} + 18q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
162.2.g.a \(72\) \(1.294\) None \(0\) \(0\) \(0\) \(0\)
162.2.g.b \(90\) \(1.294\) None \(0\) \(0\) \(0\) \(0\)

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

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