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Properties

Label 324.8.m
Level $324$
Weight $8$
Character orbit 324.m
Rep. character $\chi_{324}(13,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $1134$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 324.m (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(324, [\chi])\).

Total New Old
Modular forms 6858 1134 5724
Cusp forms 6750 1134 5616
Eisenstein series 108 0 108

Trace form

\( 1134 q + O(q^{10}) \) \( 1134 q + 186003 q^{21} + 210951 q^{23} - 416961 q^{27} + 270243 q^{29} + 154251 q^{33} - 1734993 q^{35} - 2134206 q^{41} - 1459026 q^{45} - 6232518 q^{47} + 4677309 q^{51} + 8039358 q^{53} - 3123738 q^{57} - 13283739 q^{59} + 1006938 q^{63} + 7183314 q^{65} - 13231161 q^{67} - 9814590 q^{69} - 21189672 q^{71} - 18281250 q^{75} + 24022512 q^{77} - 24623298 q^{79} + 35458488 q^{81} + 16752024 q^{83} + 11859750 q^{85} - 92159568 q^{87} - 86001201 q^{89} + 52566210 q^{93} + 91614114 q^{95} - 26124741 q^{97} - 156150594 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{8}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(324, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)