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Properties

Label 1248.2.cf
Level $1248$
Weight $2$
Character orbit 1248.cf
Rep. character $\chi_{1248}(5,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $880$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1248.cf (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1248 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1248, [\chi])\).

Total New Old
Modular forms 912 912 0
Cusp forms 880 880 0
Eisenstein series 32 32 0

Trace form

\( 880 q - 8 q^{3} + 8 q^{6} - 8 q^{9} + O(q^{10}) \) \( 880 q - 8 q^{3} + 8 q^{6} - 8 q^{9} - 24 q^{12} - 8 q^{13} - 16 q^{16} - 12 q^{18} - 8 q^{19} + 8 q^{21} + 28 q^{24} - 8 q^{27} - 16 q^{31} - 8 q^{33} + 8 q^{34} - 8 q^{37} + 20 q^{39} - 16 q^{40} - 48 q^{42} + 32 q^{43} - 24 q^{45} - 56 q^{46} - 8 q^{48} - 784 q^{49} - 8 q^{52} - 4 q^{54} + 16 q^{55} - 8 q^{57} - 80 q^{58} - 20 q^{60} - 16 q^{61} - 8 q^{63} - 8 q^{66} - 8 q^{67} + 84 q^{72} - 16 q^{73} - 40 q^{76} + 16 q^{78} + 112 q^{82} - 52 q^{84} + 32 q^{85} - 8 q^{87} + 112 q^{88} + 96 q^{91} + 32 q^{93} + 32 q^{94} + 100 q^{96} - 16 q^{97} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1248, [\chi])\) into newform subspaces

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