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Properties

Label 252.4.bj
Level $252$
Weight $4$
Character orbit 252.bj
Rep. character $\chi_{252}(103,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $280$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(252, [\chi])\).

Total New Old
Modular forms 296 296 0
Cusp forms 280 280 0
Eisenstein series 16 16 0

Trace form

\( 280 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 24 q^{6} - 8 q^{8} - 2 q^{9} + O(q^{10}) \) \( 280 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 24 q^{6} - 8 q^{8} - 2 q^{9} - 6 q^{10} + 162 q^{12} + 6 q^{14} - 2 q^{16} - 12 q^{17} + 2 q^{18} - 384 q^{20} + 118 q^{21} + 14 q^{22} + 78 q^{24} + 3102 q^{25} - 30 q^{26} + 60 q^{28} + 24 q^{29} + 101 q^{30} - 1442 q^{32} - 6 q^{33} - 24 q^{34} + 742 q^{36} - 4 q^{37} - 873 q^{38} - 378 q^{40} + 1330 q^{42} + 511 q^{44} - 666 q^{45} + 14 q^{46} + 81 q^{48} - 2 q^{49} - 763 q^{50} - 387 q^{52} - 4 q^{53} + 2247 q^{54} - 474 q^{56} - 324 q^{57} - 15 q^{58} - 1723 q^{60} - 8 q^{64} - 1468 q^{65} + 1566 q^{66} - 2358 q^{68} - 162 q^{69} + 443 q^{70} - 106 q^{72} - 12 q^{73} - 1121 q^{74} + 192 q^{76} - 1702 q^{77} + 1257 q^{78} - 4053 q^{80} + 2926 q^{81} - 30 q^{82} + 719 q^{84} - 254 q^{85} - 2759 q^{86} - 511 q^{88} + 3168 q^{89} + 3111 q^{90} + 1148 q^{92} - 162 q^{93} + 3063 q^{96} + 1915 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

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