Properties

Label 252.4.bb
Level $252$
Weight $4$
Character orbit 252.bb
Rep. character $\chi_{252}(11,\cdot)$
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.bb (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

\( 280q - 2q^{4} - 6q^{5} - 12q^{6} - 2q^{9} + O(q^{10}) \) \( 280q - 2q^{4} - 6q^{5} - 12q^{6} - 2q^{9} + 14q^{10} + 162q^{12} - 4q^{13} + 72q^{14} - 2q^{16} - 4q^{18} - 6q^{20} - 126q^{21} - 18q^{22} - 278q^{24} + 3102q^{25} + 24q^{26} + 60q^{28} - 96q^{29} - 23q^{30} + 106q^{33} - 10q^{34} - 658q^{36} - 4q^{37} + 819q^{38} - 124q^{40} - 12q^{41} + 140q^{42} - 771q^{44} - 282q^{45} - 18q^{46} + 509q^{48} - 2q^{49} + 369q^{50} - 127q^{52} - 2011q^{54} - 1032q^{56} + 308q^{57} + 17q^{58} + 1457q^{60} - 4q^{61} - 8q^{64} + 564q^{66} + 1968q^{68} - 2118q^{69} - 945q^{70} - 2962q^{72} - 4q^{73} - 2685q^{74} - 66q^{76} + 978q^{77} - 821q^{78} + 3297q^{80} + 3230q^{81} - 10q^{82} - 3775q^{84} - 254q^{85} + 9q^{86} + 513q^{88} + 3180q^{89} + 1199q^{90} + 3984q^{92} + 270q^{93} - 66q^{94} - 2669q^{96} - 4q^{97} - 4515q^{98} + O(q^{100}) \)

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

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