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Properties

Label 1148.2.cl
Level $1148$
Weight $2$
Character orbit 1148.cl
Rep. character $\chi_{1148}(11,\cdot)$
Character field $\Q(\zeta_{120})$
Dimension $5248$
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.cl (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1148 \)
Character field: \(\Q(\zeta_{120})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 5504 5504 0
Cusp forms 5248 5248 0
Eisenstein series 256 256 0

Trace form

\( 5248 q - 16 q^{2} - 20 q^{4} - 32 q^{5} - 64 q^{6} - 64 q^{8} - 32 q^{9} + O(q^{10}) \) \( 5248 q - 16 q^{2} - 20 q^{4} - 32 q^{5} - 64 q^{6} - 64 q^{8} - 32 q^{9} - 12 q^{10} - 40 q^{12} - 128 q^{13} - 44 q^{14} - 12 q^{16} - 32 q^{17} - 12 q^{18} - 80 q^{20} - 64 q^{21} - 16 q^{22} + 8 q^{24} - 40 q^{25} - 16 q^{26} - 48 q^{28} - 128 q^{29} + 8 q^{30} - 36 q^{32} - 32 q^{33} - 64 q^{34} - 32 q^{36} - 24 q^{37} - 4 q^{38} - 128 q^{41} - 64 q^{42} - 48 q^{44} - 40 q^{45} - 72 q^{46} - 200 q^{48} - 32 q^{49} - 88 q^{50} + 72 q^{52} - 32 q^{53} + 64 q^{54} - 48 q^{56} - 96 q^{57} + 12 q^{58} - 40 q^{60} - 32 q^{61} - 80 q^{62} - 80 q^{64} - 48 q^{65} - 20 q^{66} + 52 q^{68} - 176 q^{69} + 4 q^{70} - 20 q^{72} - 32 q^{73} + 12 q^{74} - 384 q^{76} - 64 q^{77} + 160 q^{78} - 44 q^{80} + 176 q^{82} - 200 q^{84} - 64 q^{85} - 20 q^{86} - 60 q^{88} - 32 q^{89} - 640 q^{90} - 224 q^{92} - 80 q^{93} + 116 q^{94} + 200 q^{96} - 128 q^{97} + 28 q^{98} + O(q^{100}) \)

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.