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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

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

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.