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Properties

Label 2448.4.dn
Level $2448$
Weight $4$
Character orbit 2448.dn
Rep. character $\chi_{2448}(205,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $4608$
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.dn (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 5200 4608 592
Cusp forms 5168 4608 560
Eisenstein series 32 0 32

Trace form

\( 4608 q - 60 q^{6} + O(q^{10}) \) \( 4608 q - 60 q^{6} - 312 q^{12} + 308 q^{20} - 736 q^{24} - 1088 q^{26} + 264 q^{27} + 1112 q^{30} - 800 q^{36} - 2408 q^{38} + 680 q^{42} + 3080 q^{44} + 40 q^{48} + 112896 q^{49} + 6156 q^{54} - 2000 q^{56} - 1188 q^{58} - 2040 q^{59} - 7452 q^{60} - 7256 q^{62} - 1080 q^{64} + 8792 q^{66} + 6608 q^{75} + 3320 q^{78} - 9280 q^{80} + 2808 q^{82} - 18520 q^{84} - 2780 q^{86} - 4176 q^{88} + 4680 q^{90} - 4272 q^{93} + 12160 q^{95} + 592 q^{96} + 5312 q^{99} + O(q^{100}) \)

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

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