↑

Properties

Label 864.3.bd
Level $864$
Weight $3$
Character orbit 864.bd
Rep. character $\chi_{864}(79,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $420$
Sturm bound $432$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 864.bd (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
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 444 1332
Cusp forms 1680 420 1260
Eisenstein series 96 24 72

Trace form

\( 420 q + 12 q^{3} - 12 q^{9} + O(q^{10}) \) \( 420 q + 12 q^{3} - 12 q^{9} + 12 q^{11} - 6 q^{17} + 6 q^{19} - 12 q^{25} + 12 q^{27} + 12 q^{33} + 6 q^{35} + 60 q^{41} + 12 q^{43} - 12 q^{49} - 42 q^{51} + 42 q^{57} - 420 q^{59} - 12 q^{65} + 12 q^{67} - 6 q^{73} + 348 q^{75} - 12 q^{81} + 732 q^{83} - 6 q^{89} + 6 q^{91} - 12 q^{97} + 12 q^{99} + O(q^{100}) \)

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

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