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

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

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

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