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Properties

Label 2448.2.do
Level $2448$
Weight $2$
Character orbit 2448.do
Rep. character $\chi_{2448}(157,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1712$
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.do (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2448 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1744 1744 0
Cusp forms 1712 1712 0
Eisenstein series 32 32 0

Trace form

\( 1712 q - 8 q^{3} - 4 q^{4} + O(q^{10}) \) \( 1712 q - 8 q^{3} - 4 q^{4} - 16 q^{10} - 4 q^{11} + 12 q^{12} - 4 q^{13} + 16 q^{14} - 4 q^{16} - 16 q^{17} - 18 q^{20} - 8 q^{21} + 6 q^{22} - 36 q^{24} + 824 q^{25} - 8 q^{27} - 24 q^{28} - 4 q^{29} - 36 q^{30} - 4 q^{31} + 20 q^{32} - 16 q^{33} + 2 q^{34} - 16 q^{35} - 4 q^{38} + 12 q^{39} + 20 q^{40} + 52 q^{42} + 8 q^{44} + 24 q^{46} + 72 q^{47} + 28 q^{48} + 12 q^{50} - 36 q^{51} - 4 q^{52} - 36 q^{54} - 16 q^{56} - 24 q^{57} + 6 q^{58} + 52 q^{60} + 44 q^{62} + 20 q^{63} - 16 q^{64} - 4 q^{65} + 36 q^{66} - 4 q^{67} - 10 q^{68} - 8 q^{69} - 40 q^{70} - 72 q^{72} + 30 q^{74} - 16 q^{75} + 56 q^{77} - 156 q^{78} - 4 q^{79} - 148 q^{80} - 16 q^{81} - 8 q^{84} + 8 q^{85} + 16 q^{86} + 24 q^{87} - 18 q^{88} - 74 q^{90} - 72 q^{91} - 36 q^{92} + 12 q^{93} - 4 q^{95} - 46 q^{96} - 4 q^{97} + 104 q^{98} + 28 q^{99} + O(q^{100}) \)

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.