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Properties

Label 1148.4.cg
Level $1148$
Weight $4$
Character orbit 1148.cg
Rep. character $\chi_{1148}(87,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $8000$
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.cg (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1148 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 8128 8128 0
Cusp forms 8000 8000 0
Eisenstein series 128 128 0

Trace form

\( 8000 q - 10 q^{2} - 6 q^{4} - 60 q^{5} - 40 q^{8} + O(q^{10}) \) \( 8000 q - 10 q^{2} - 6 q^{4} - 60 q^{5} - 40 q^{8} - 18 q^{10} - 24 q^{12} - 98 q^{14} - 6 q^{16} - 48 q^{17} - 102 q^{18} - 40 q^{21} + 440 q^{22} - 402 q^{24} + 24188 q^{25} + 774 q^{26} + 1226 q^{28} - 512 q^{29} + 730 q^{30} - 60 q^{33} - 1320 q^{36} - 12 q^{37} + 3210 q^{38} - 1548 q^{40} + 1320 q^{42} + 248 q^{44} - 36 q^{45} + 2090 q^{46} - 40 q^{49} - 2892 q^{52} - 16 q^{53} - 9708 q^{54} + 3930 q^{56} - 48 q^{57} - 710 q^{58} + 1930 q^{60} - 60 q^{61} + 3840 q^{64} + 764 q^{65} + 9882 q^{66} - 7722 q^{68} + 9674 q^{70} - 2702 q^{72} - 10 q^{74} - 40 q^{77} - 3280 q^{78} - 30 q^{80} + 309392 q^{81} + 23352 q^{82} - 8660 q^{84} + 1528 q^{85} + 26 q^{86} + 2682 q^{88} - 6408 q^{89} - 9956 q^{92} + 680 q^{93} + 30702 q^{94} - 24852 q^{96} + 9726 q^{98} + O(q^{100}) \)

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.