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Properties

Label 1148.2.bw
Level $1148$
Weight $2$
Character orbit 1148.bw
Rep. character $\chi_{1148}(31,\cdot)$
Character field $\Q(\zeta_{30})$
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.bw (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1148 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 1312 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 24 q^{8} + 608 q^{9} + O(q^{10}) \) \( 1312 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 24 q^{8} + 608 q^{9} - 36 q^{10} - 15 q^{12} - 3 q^{16} - 30 q^{17} + 18 q^{18} - 38 q^{21} - 20 q^{22} - 60 q^{24} - 154 q^{25} - 15 q^{26} + 15 q^{28} - 35 q^{30} - 18 q^{32} - 18 q^{33} + 94 q^{36} - 6 q^{37} + 66 q^{40} - 40 q^{42} - 96 q^{45} + 50 q^{46} + 4 q^{49} + 8 q^{50} - 15 q^{52} - 10 q^{53} + 105 q^{54} + 60 q^{56} - 60 q^{57} - 5 q^{58} + 60 q^{60} - 18 q^{61} + 72 q^{64} - 10 q^{65} - 90 q^{66} - 85 q^{70} - 109 q^{72} - 48 q^{73} - 75 q^{74} - 40 q^{77} + 118 q^{78} - 27 q^{80} - 536 q^{81} - 117 q^{82} + 91 q^{84} - 23 q^{86} - 330 q^{89} + 18 q^{92} - 30 q^{93} - 105 q^{94} + 82 q^{98} + O(q^{100}) \)

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.