Properties

Label 2304.2.bt
Level $2304$
Weight $2$
Character orbit 2304.bt
Rep. character $\chi_{2304}(37,\cdot)$
Character field $\Q(\zeta_{64})$
Dimension $5088$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2304.bt (of order \(64\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 256 \)
Character field: \(\Q(\zeta_{64})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2304, [\chi])\).

Total New Old
Modular forms 12416 5152 7264
Cusp forms 12160 5088 7072
Eisenstein series 256 64 192

Trace form

\( 5088q + 32q^{2} - 32q^{4} + 32q^{5} - 32q^{7} + 32q^{8} + O(q^{10}) \) \( 5088q + 32q^{2} - 32q^{4} + 32q^{5} - 32q^{7} + 32q^{8} - 32q^{10} + 32q^{11} - 32q^{13} + 32q^{14} - 32q^{16} + 32q^{17} - 32q^{19} + 32q^{20} - 32q^{22} + 32q^{23} - 32q^{25} + 32q^{26} - 32q^{28} + 32q^{29} - 32q^{31} + 32q^{32} - 32q^{34} + 32q^{35} - 32q^{37} + 32q^{38} - 32q^{40} + 32q^{41} - 32q^{43} + 32q^{44} - 32q^{46} + 32q^{47} - 32q^{49} + 32q^{50} - 32q^{52} + 32q^{53} - 32q^{55} + 32q^{56} - 32q^{58} + 32q^{59} - 32q^{61} + 32q^{62} - 32q^{64} + 32q^{65} - 32q^{67} + 32q^{68} - 32q^{70} + 32q^{71} - 32q^{73} + 32q^{74} - 32q^{76} + 32q^{77} - 32q^{79} + 32q^{80} - 32q^{82} + 32q^{83} - 32q^{85} + 32q^{86} - 32q^{88} + 32q^{89} - 32q^{91} + 32q^{92} - 32q^{94} + 32q^{95} - 32q^{97} + 32q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database