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Properties

Label 324.4.m
Level $324$
Weight $4$
Character orbit 324.m
Rep. character $\chi_{324}(13,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $486$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 324.m (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(324, [\chi])\).

Total New Old
Modular forms 2970 486 2484
Cusp forms 2862 486 2376
Eisenstein series 108 0 108

Trace form

\( 486 q + O(q^{10}) \) \( 486 q + 108 q^{21} - 378 q^{23} - 702 q^{27} - 540 q^{29} + 432 q^{33} + 1242 q^{35} - 1854 q^{41} - 1026 q^{45} + 594 q^{47} + 2961 q^{51} + 2862 q^{53} + 2214 q^{57} + 1449 q^{59} - 1998 q^{63} - 10026 q^{65} + 2754 q^{67} - 7110 q^{69} - 720 q^{71} + 4500 q^{75} + 9792 q^{77} - 4212 q^{79} + 5760 q^{81} + 5328 q^{83} - 3240 q^{85} + 5472 q^{87} - 1395 q^{89} - 7326 q^{93} - 12006 q^{95} + 5184 q^{97} - 7542 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(324, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)