Properties

Label 864.2.bn
Level 864
Weight 2
Character orbit bn
Rep. character \(\chi_{864}(35,\cdot)\)
Character field \(\Q(\zeta_{24})\)
Dimension 368
Newform subspaces 1
Sturm bound 288
Trace bound 0

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Defining parameters

Level: \( N \) = \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 864.bn (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 288 \)
Character field: \(\Q(\zeta_{24})\)
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 1200 400 800
Cusp forms 1104 368 736
Eisenstein series 96 32 64

Trace form

\( 368q + 12q^{2} - 4q^{4} + 12q^{5} - 4q^{7} + O(q^{10}) \) \( 368q + 12q^{2} - 4q^{4} + 12q^{5} - 4q^{7} - 16q^{10} + 12q^{11} - 4q^{13} + 12q^{14} - 4q^{16} - 16q^{19} + 12q^{20} - 4q^{22} + 12q^{23} - 4q^{25} - 16q^{28} + 12q^{29} + 12q^{32} - 12q^{34} - 16q^{37} + 12q^{38} - 4q^{40} + 12q^{41} - 4q^{43} - 16q^{46} + 24q^{47} + 168q^{50} - 4q^{52} - 16q^{55} + 12q^{56} + 32q^{58} + 12q^{59} - 4q^{61} - 16q^{64} + 24q^{65} - 4q^{67} + 60q^{68} - 4q^{70} - 16q^{73} + 12q^{74} - 28q^{76} + 12q^{77} - 8q^{79} - 16q^{82} + 132q^{83} - 24q^{85} + 12q^{86} - 4q^{88} - 16q^{91} - 216q^{92} - 20q^{94} - 8q^{97} + O(q^{100}) \)

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.bn.a \(368\) \(6.899\) None \(12\) \(0\) \(12\) \(-4\)

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

\( S_{2}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database