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Properties

Label 1148.4.bu
Level $1148$
Weight $4$
Character orbit 1148.bu
Rep. character $\chi_{1148}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $4000$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1148.bu (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1148 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1148, [\chi])\).

Total New Old
Modular forms 4064 4064 0
Cusp forms 4000 4000 0
Eisenstein series 64 64 0

Trace form

\( 4000 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 96 q^{8} - 17728 q^{9} + O(q^{10}) \) \( 4000 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 96 q^{8} - 17728 q^{9} - 36 q^{10} - 9 q^{12} - 66 q^{14} - 3 q^{16} - 18 q^{17} - 36 q^{18} + 14 q^{21} + 524 q^{22} - 306 q^{24} - 12106 q^{25} - 807 q^{26} - 517 q^{28} + 144 q^{29} - 687 q^{30} + 382 q^{32} - 18 q^{33} + 3074 q^{36} - 6 q^{37} + 3210 q^{38} + 3066 q^{40} + 1196 q^{42} + 248 q^{44} + 1788 q^{45} - 1126 q^{46} - 220 q^{49} + 624 q^{50} - 2877 q^{52} - 6 q^{53} - 2589 q^{54} - 4742 q^{56} + 300 q^{57} - 673 q^{58} - 2942 q^{60} - 18 q^{61} + 72 q^{64} - 226 q^{65} + 684 q^{66} - 7722 q^{68} - 5993 q^{70} + 3447 q^{72} - 48 q^{73} + 329 q^{74} + 1360 q^{77} + 4138 q^{78} - 3771 q^{80} - 149000 q^{81} + 6873 q^{82} - 2511 q^{84} + 3528 q^{85} + 3661 q^{86} + 1010 q^{88} - 9558 q^{89} - 470 q^{92} + 1686 q^{93} - 4005 q^{94} - 24852 q^{96} + 3272 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1148, [\chi])\) into newform subspaces

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