Properties

Label 2448.2.bk
Level $2448$
Weight $2$
Character orbit 2448.bk
Rep. character $\chi_{2448}(1189,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $356$
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.bk (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 272 \)
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 880 364 516
Cusp forms 848 356 492
Eisenstein series 32 8 24

Trace form

\( 356 q + 4 q^{2} - 4 q^{4} + 4 q^{8} + O(q^{10}) \) \( 356 q + 4 q^{2} - 4 q^{4} + 4 q^{8} - 4 q^{13} - 12 q^{16} + 4 q^{17} - 20 q^{19} + 4 q^{26} + 4 q^{32} + 24 q^{34} + 24 q^{35} - 4 q^{38} - 4 q^{43} - 32 q^{47} + 324 q^{49} - 56 q^{50} - 12 q^{52} + 4 q^{53} + 36 q^{59} + 20 q^{64} - 4 q^{67} + 72 q^{68} - 48 q^{70} - 20 q^{76} + 32 q^{77} + 44 q^{83} + 24 q^{85} - 52 q^{86} - 160 q^{94} + 92 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(816, [\chi])\)\(^{\oplus 2}\)