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Properties

Label 2448.2.dr
Level $2448$
Weight $2$
Character orbit 2448.dr
Rep. character $\chi_{2448}(659,\cdot)$
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.dr (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

\( 1712 q - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} + O(q^{10}) \) \( 1712 q - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} + 24 q^{14} - 24 q^{15} - 4 q^{16} - 16 q^{18} - 6 q^{20} - 8 q^{21} - 10 q^{22} - 12 q^{23} + 28 q^{24} + 824 q^{25} - 8 q^{27} + 8 q^{28} + 4 q^{30} - 60 q^{32} - 16 q^{33} - 6 q^{34} - 16 q^{37} - 12 q^{38} - 8 q^{39} - 4 q^{40} - 52 q^{42} - 28 q^{45} - 24 q^{46} + 28 q^{48} - 12 q^{50} - 12 q^{51} - 4 q^{52} + 8 q^{54} - 32 q^{55} - 48 q^{56} - 24 q^{57} + 6 q^{58} - 92 q^{60} - 4 q^{61} + 80 q^{63} - 16 q^{64} - 12 q^{65} - 12 q^{66} - 4 q^{67} + 18 q^{68} - 8 q^{69} - 40 q^{70} + 56 q^{72} + 66 q^{74} - 16 q^{75} - 52 q^{78} - 16 q^{81} - 16 q^{82} - 8 q^{84} + 8 q^{85} + 48 q^{86} + 14 q^{88} - 186 q^{90} + 40 q^{91} - 120 q^{92} + 12 q^{93} - 60 q^{95} + 46 q^{96} - 4 q^{97} - 44 q^{99} + O(q^{100}) \)

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.