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Properties

Label 2448.2.cj
Level $2448$
Weight $2$
Character orbit 2448.cj
Rep. character $\chi_{2448}(253,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $712$
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.cj (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 272 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1760 728 1032
Cusp forms 1696 712 984
Eisenstein series 64 16 48

Trace form

\( 712 q + 4 q^{2} + 4 q^{5} + 4 q^{8} + O(q^{10}) \) \( 712 q + 4 q^{2} + 4 q^{5} + 4 q^{8} - 12 q^{10} + 4 q^{11} + 40 q^{14} - 8 q^{16} + 8 q^{17} + 4 q^{20} + 12 q^{22} + 12 q^{26} - 12 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} - 20 q^{34} + 8 q^{35} - 4 q^{37} - 16 q^{38} + 64 q^{40} + 40 q^{44} - 20 q^{46} - 8 q^{49} + 8 q^{50} - 8 q^{52} + 8 q^{53} - 64 q^{55} - 40 q^{56} + 4 q^{58} - 36 q^{61} + 64 q^{62} + 24 q^{65} - 8 q^{67} - 104 q^{68} - 72 q^{70} + 68 q^{74} + 16 q^{76} + 8 q^{77} - 8 q^{79} - 40 q^{80} + 20 q^{82} - 4 q^{85} - 64 q^{86} + 24 q^{88} - 48 q^{91} + 20 q^{92} - 24 q^{94} + 8 q^{95} - 8 q^{97} + 16 q^{98} + O(q^{100}) \)

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

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