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Properties

Label 2448.2.fm
Level $2448$
Weight $2$
Character orbit 2448.fm
Rep. character $\chi_{2448}(29,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $6848$
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.fm (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2448 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 6976 6976 0
Cusp forms 6848 6848 0
Eisenstein series 128 128 0

Trace form

\( 6848 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} + O(q^{10}) \) \( 6848 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 32 q^{10} - 24 q^{11} + 8 q^{12} - 24 q^{14} - 32 q^{15} - 32 q^{18} - 32 q^{19} - 24 q^{20} - 8 q^{22} - 16 q^{24} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 16 q^{31} - 24 q^{32} - 8 q^{34} - 16 q^{36} - 32 q^{37} - 24 q^{38} - 48 q^{39} - 8 q^{40} - 8 q^{43} - 16 q^{45} - 32 q^{46} - 48 q^{47} - 16 q^{48} - 16 q^{49} - 96 q^{51} - 16 q^{52} - 16 q^{54} - 24 q^{56} - 8 q^{58} - 24 q^{59} - 16 q^{60} - 8 q^{61} - 32 q^{63} - 32 q^{64} - 48 q^{65} - 24 q^{68} - 32 q^{69} - 8 q^{70} - 120 q^{72} - 24 q^{74} - 16 q^{75} - 40 q^{76} - 24 q^{77} - 64 q^{78} - 16 q^{79} - 32 q^{81} - 32 q^{82} - 264 q^{83} - 64 q^{84} - 8 q^{85} - 288 q^{86} - 8 q^{88} - 200 q^{90} - 144 q^{91} - 24 q^{92} - 16 q^{93} - 8 q^{94} - 48 q^{95} - 224 q^{96} - 16 q^{97} - 16 q^{99} + O(q^{100}) \)

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.