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Properties

Label 2448.4.bm
Level $2448$
Weight $4$
Character orbit 2448.bm
Rep. character $\chi_{2448}(829,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1076$
Sturm bound $1728$

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Defining parameters

Level: \( N \) \(=\) \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2448.bm (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 272 \)
Character field: \(\Q(i)\)
Sturm bound: \(1728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2448, [\chi])\).

Total New Old
Modular forms 2608 1084 1524
Cusp forms 2576 1076 1500
Eisenstein series 32 8 24

Trace form

\( 1076 q - 4 q^{4} + 4 q^{5} + O(q^{10}) \) \( 1076 q - 4 q^{4} + 4 q^{5} - 78 q^{10} - 4 q^{13} + 72 q^{14} + 260 q^{16} + 4 q^{17} + 170 q^{20} + 266 q^{22} + 26500 q^{25} + 500 q^{26} - 460 q^{28} - 4 q^{31} - 460 q^{32} + 194 q^{34} + 4 q^{35} - 4 q^{37} + 4 q^{38} - 662 q^{40} + 806 q^{44} - 116 q^{46} - 1872 q^{47} + 36 q^{50} - 1660 q^{52} + 1472 q^{56} + 158 q^{58} - 1376 q^{59} - 1828 q^{61} + 916 q^{62} + 1508 q^{64} - 484 q^{65} - 4 q^{67} + 874 q^{68} - 1580 q^{70} + 296 q^{73} - 490 q^{74} + 2352 q^{76} - 1372 q^{77} - 2836 q^{79} - 734 q^{80} - 4840 q^{82} - 12 q^{85} + 472 q^{86} - 410 q^{88} + 3232 q^{92} + 648 q^{94} + 4 q^{95} - 4 q^{97} - 6080 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2448, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2448, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2448, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(816, [\chi])\)\(^{\oplus 2}\)