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Properties

Label 1148.4.bw
Level $1148$
Weight $4$
Character orbit 1148.bw
Rep. character $\chi_{1148}(31,\cdot)$
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.bw (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

\( 4000 q - 3 q^{2} - 3 q^{4} - 18 q^{5} + 72 q^{8} + 17696 q^{9} + O(q^{10}) \) \( 4000 q - 3 q^{2} - 3 q^{4} - 18 q^{5} + 72 q^{8} + 17696 q^{9} + 18 q^{10} - 15 q^{12} - 3 q^{16} - 30 q^{17} + 126 q^{18} - 38 q^{21} - 20 q^{22} - 420 q^{24} - 12106 q^{25} - 15 q^{26} - 485 q^{28} + 240 q^{29} - 275 q^{30} + 382 q^{32} - 18 q^{33} - 2330 q^{36} - 6 q^{37} - 1614 q^{40} - 2580 q^{42} - 1824 q^{45} - 76 q^{46} - 220 q^{49} + 248 q^{50} - 15 q^{52} - 10 q^{53} + 3345 q^{54} - 3300 q^{56} - 348 q^{57} - 5 q^{58} + 3180 q^{60} - 18 q^{61} - 3960 q^{64} - 10 q^{65} - 10602 q^{66} + 13515 q^{70} - 757 q^{72} - 48 q^{73} + 1757 q^{74} - 1384 q^{77} + 7270 q^{78} - 3771 q^{80} - 148136 q^{81} + 16383 q^{82} - 1301 q^{84} - 3699 q^{86} - 3400 q^{88} + 15870 q^{89} + 10170 q^{92} - 2830 q^{93} - 17565 q^{94} + 6390 q^{98} + O(q^{100}) \)

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.