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Properties

Label 1148.2.bp
Level $1148$
Weight $2$
Character orbit 1148.bp
Rep. character $\chi_{1148}(79,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $1312$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.bp (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1148 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1148, [\chi])\).

Total New Old
Modular forms 1376 1376 0
Cusp forms 1312 1312 0
Eisenstein series 64 64 0

Trace form

\( 1312 q - 4 q^{2} - 8 q^{5} - 16 q^{6} - 16 q^{8} - 8 q^{9} + O(q^{10}) \) \( 1312 q - 4 q^{2} - 8 q^{5} - 16 q^{6} - 16 q^{8} - 8 q^{9} - 8 q^{10} + 20 q^{12} - 32 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 16 q^{21} - 64 q^{22} - 28 q^{24} - 4 q^{26} + 8 q^{28} - 32 q^{29} - 28 q^{30} + 16 q^{32} - 8 q^{33} - 16 q^{34} - 48 q^{36} - 16 q^{37} - 16 q^{38} - 32 q^{41} - 16 q^{42} + 28 q^{44} + 52 q^{46} + 120 q^{48} - 48 q^{49} + 8 q^{50} - 92 q^{52} - 8 q^{53} - 84 q^{54} + 8 q^{56} - 64 q^{57} - 32 q^{58} + 20 q^{60} - 8 q^{61} + 8 q^{65} + 28 q^{68} + 16 q^{69} - 244 q^{70} - 8 q^{73} - 32 q^{74} - 296 q^{76} - 16 q^{77} - 240 q^{78} + 24 q^{80} + 44 q^{82} - 80 q^{84} - 96 q^{85} + 40 q^{88} - 8 q^{89} - 40 q^{90} + 144 q^{92} + 40 q^{93} - 136 q^{94} - 20 q^{96} - 32 q^{97} - 168 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1148, [\chi])\) into newform subspaces

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