Properties

Label 864.2.bk
Level 864
Weight 2
Character orbit bk
Rep. character \(\chi_{864}(37,\cdot)\)
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.bk (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

\( 368q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 16q^{8} + O(q^{10}) \) \( 368q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 16q^{8} - 16q^{10} + 4q^{11} - 4q^{13} + 4q^{14} - 4q^{16} - 16q^{19} + 4q^{20} - 4q^{22} + 4q^{23} - 4q^{25} + 16q^{26} - 16q^{28} + 4q^{29} - 8q^{31} + 4q^{32} + 4q^{34} + 16q^{35} - 16q^{37} + 60q^{38} - 4q^{40} + 4q^{41} - 4q^{43} + 104q^{44} - 16q^{46} - 48q^{50} - 4q^{52} + 16q^{53} - 16q^{55} + 84q^{56} - 40q^{58} + 4q^{59} - 4q^{61} + 24q^{62} - 16q^{64} + 8q^{65} - 4q^{67} - 12q^{68} - 4q^{70} + 16q^{71} - 16q^{73} + 4q^{74} + 20q^{76} + 4q^{77} - 48q^{80} - 16q^{82} - 36q^{83} + 16q^{85} - 100q^{86} - 4q^{88} + 16q^{89} - 16q^{91} + 80q^{92} - 20q^{94} + 136q^{95} - 8q^{97} - 104q^{98} + O(q^{100}) \)

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.bk.a \(368\) \(6.899\) None \(4\) \(0\) \(4\) \(-4\)

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