Properties

Label 864.2.bi
Level 864
Weight 2
Character orbit bi
Rep. character \(\chi_{864}(95,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 216
Newform subspaces 1
Sturm bound 288
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 864.bi (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 108 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(864, [\chi])\).

Total New Old
Modular forms 912 216 696
Cusp forms 816 216 600
Eisenstein series 96 0 96

Trace form

\( 216q + O(q^{10}) \) \( 216q - 24q^{29} + 36q^{33} + 36q^{41} - 24q^{45} + 12q^{57} + 48q^{65} + 48q^{69} + 48q^{77} + 48q^{81} + 36q^{89} - 144q^{93} - 36q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
864.2.bi.a \(216\) \(6.899\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database