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Properties

Label 2448.2.v
Level $2448$
Weight $2$
Character orbit 2448.v
Rep. character $\chi_{2448}(613,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $320$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2448.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2448, [\chi])\).

Total New Old
Modular forms 880 320 560
Cusp forms 848 320 528
Eisenstein series 32 0 32

Trace form

\( 320 q - 4 q^{4} - 12 q^{8} + O(q^{10}) \) \( 320 q - 4 q^{4} - 12 q^{8} - 12 q^{10} - 8 q^{11} - 4 q^{14} + 4 q^{16} + 28 q^{20} - 12 q^{22} + 52 q^{26} - 16 q^{29} + 24 q^{31} - 20 q^{32} + 24 q^{35} - 16 q^{37} - 28 q^{38} + 60 q^{40} + 40 q^{43} - 40 q^{44} - 320 q^{49} - 36 q^{50} - 20 q^{52} + 16 q^{53} - 12 q^{56} + 32 q^{58} + 24 q^{59} - 4 q^{62} - 76 q^{64} - 16 q^{67} - 24 q^{70} + 28 q^{74} + 20 q^{76} + 16 q^{77} - 40 q^{79} - 20 q^{80} - 36 q^{82} - 40 q^{83} + 20 q^{86} - 76 q^{88} + 8 q^{92} - 32 q^{94} - 112 q^{95} - 24 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2448, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2448, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)