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Properties

Label 1148.4.cl
Level $1148$
Weight $4$
Character orbit 1148.cl
Rep. character $\chi_{1148}(11,\cdot)$
Character field $\Q(\zeta_{120})$
Dimension $16000$
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.cl (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1148 \)
Character field: \(\Q(\zeta_{120})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 16256 16256 0
Cusp forms 16000 16000 0
Eisenstein series 256 256 0

Trace form

\( 16000 q - 16 q^{2} - 20 q^{4} - 32 q^{5} - 64 q^{6} - 64 q^{8} - 32 q^{9} + O(q^{10}) \) \( 16000 q - 16 q^{2} - 20 q^{4} - 32 q^{5} - 64 q^{6} - 64 q^{8} - 32 q^{9} - 12 q^{10} - 232 q^{12} - 128 q^{13} - 164 q^{14} - 12 q^{16} - 32 q^{17} - 12 q^{18} - 944 q^{20} - 64 q^{21} - 1072 q^{22} - 376 q^{24} - 40 q^{25} - 16 q^{26} - 288 q^{28} - 128 q^{29} + 200 q^{30} + 764 q^{32} - 32 q^{33} - 64 q^{34} + 448 q^{36} - 24 q^{37} - 620 q^{38} - 128 q^{41} - 64 q^{42} - 528 q^{44} - 40 q^{45} + 760 q^{46} - 8 q^{48} - 480 q^{49} - 1000 q^{50} + 1144 q^{52} - 32 q^{53} - 2768 q^{54} + 4048 q^{56} - 96 q^{57} - 1388 q^{58} - 2200 q^{60} - 32 q^{61} - 128 q^{62} - 80 q^{64} - 592 q^{65} - 20 q^{66} + 11524 q^{68} - 560 q^{69} - 17260 q^{70} - 20 q^{72} - 32 q^{73} - 2236 q^{74} + 18720 q^{76} - 64 q^{77} + 8128 q^{78} + 1492 q^{80} - 15568 q^{82} + 16840 q^{84} - 5312 q^{85} - 20 q^{86} + 292 q^{88} - 32 q^{89} - 2512 q^{90} + 160 q^{92} - 464 q^{93} - 7396 q^{94} + 24712 q^{96} - 128 q^{97} - 3532 q^{98} + O(q^{100}) \)

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.