Properties

Label 324.2.m
Level $324$
Weight $2$
Character orbit 324.m
Rep. character $\chi_{324}(13,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $162$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 324.m (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Newform subspaces: \( 1 \)
Sturm bound: \(108\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(324, [\chi])\).

Total New Old
Modular forms 1026 162 864
Cusp forms 918 162 756
Eisenstein series 108 0 108

Trace form

\( 162q + O(q^{10}) \) \( 162q + 27q^{21} + 27q^{23} + 27q^{27} + 27q^{29} + 27q^{33} + 27q^{35} - 18q^{41} - 54q^{45} - 54q^{47} - 63q^{51} - 54q^{53} - 54q^{57} - 63q^{59} - 54q^{63} - 90q^{65} + 27q^{67} - 90q^{69} - 72q^{71} - 90q^{75} - 144q^{77} + 54q^{79} - 72q^{81} - 72q^{83} + 54q^{85} - 144q^{87} - 99q^{89} - 90q^{93} - 126q^{95} + 27q^{97} - 90q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
324.2.m.a \(162\) \(2.587\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(324, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)