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Properties

Label 864.3.be
Level $864$
Weight $3$
Character orbit 864.be
Rep. character $\chi_{864}(31,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $432$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 864.be (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 108 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(864, [\chi])\).

Total New Old
Modular forms 1776 432 1344
Cusp forms 1680 432 1248
Eisenstein series 96 0 96

Trace form

\( 432 q + O(q^{10}) \) \( 432 q + 144 q^{29} - 72 q^{33} + 216 q^{41} - 240 q^{45} - 168 q^{57} - 288 q^{65} - 96 q^{69} + 288 q^{77} + 480 q^{81} - 216 q^{89} + 2016 q^{93} + 360 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)