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Properties

Label 2448.2.du
Level $2448$
Weight $2$
Character orbit 2448.du
Rep. character $\chi_{2448}(91,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1424$
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.du (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 272 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 3520 1456 2064
Cusp forms 3392 1424 1968
Eisenstein series 128 32 96

Trace form

\( 1424 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 16 q^{7} + 8 q^{8} + O(q^{10}) \) \( 1424 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 16 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} + 8 q^{14} + 16 q^{17} - 40 q^{19} - 24 q^{20} - 8 q^{22} + 16 q^{23} - 8 q^{26} + 40 q^{28} + 8 q^{29} + 8 q^{32} - 8 q^{34} + 16 q^{35} - 8 q^{37} + 48 q^{38} - 16 q^{40} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 16 q^{49} + 80 q^{50} - 16 q^{52} + 8 q^{53} - 16 q^{55} + 8 q^{56} + 56 q^{58} + 8 q^{59} + 56 q^{61} + 48 q^{62} + 40 q^{64} - 16 q^{65} + 8 q^{68} + 56 q^{70} + 16 q^{71} + 8 q^{74} + 24 q^{76} + 8 q^{77} + 8 q^{80} - 104 q^{82} + 88 q^{83} - 8 q^{85} + 96 q^{86} - 8 q^{88} + 48 q^{91} - 72 q^{92} + 104 q^{94} - 16 q^{97} - 128 q^{98} + O(q^{100}) \)

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

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