Properties

Label 2448.2.et
Level $2448$
Weight $2$
Character orbit 2448.et
Rep. character $\chi_{2448}(349,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $3424$
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.et (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2448 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 3488 3488 0
Cusp forms 3424 3424 0
Eisenstein series 64 64 0

Trace form

\( 3424 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{8} + O(q^{10}) \) \( 3424 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{8} - 32 q^{10} - 4 q^{11} + 12 q^{12} + 16 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 4 q^{20} - 20 q^{22} + 56 q^{24} - 8 q^{27} + 16 q^{28} - 4 q^{29} - 8 q^{31} - 4 q^{32} - 32 q^{33} - 4 q^{34} - 32 q^{35} + 8 q^{36} - 16 q^{37} - 16 q^{38} + 24 q^{42} - 8 q^{43} - 16 q^{44} + 12 q^{45} - 64 q^{46} - 60 q^{48} - 8 q^{49} - 8 q^{50} + 32 q^{51} - 8 q^{52} + 36 q^{54} - 4 q^{56} - 48 q^{57} + 12 q^{58} - 8 q^{59} + 80 q^{60} - 4 q^{61} - 136 q^{62} - 16 q^{63} - 8 q^{65} - 172 q^{66} - 8 q^{67} + 96 q^{68} - 16 q^{69} - 12 q^{70} - 40 q^{72} - 52 q^{74} - 40 q^{75} - 20 q^{76} + 72 q^{78} - 8 q^{79} - 16 q^{80} - 16 q^{82} + 72 q^{83} - 16 q^{84} - 4 q^{85} + 32 q^{86} - 36 q^{88} + 60 q^{90} + 40 q^{91} + 28 q^{92} - 20 q^{94} - 8 q^{95} + 4 q^{96} - 8 q^{97} + 28 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2448, [\chi])\) into newform subspaces

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