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Properties

Label 252.12.bb
Level $252$
Weight $12$
Character orbit 252.bb
Rep. character $\chi_{252}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1048$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 252.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(252, [\chi])\).

Total New Old
Modular forms 1064 1064 0
Cusp forms 1048 1048 0
Eisenstein series 16 16 0

Trace form

\( 1048 q - 2 q^{4} - 6 q^{5} - 2052 q^{6} - 2 q^{9} + O(q^{10}) \) \( 1048 q - 2 q^{4} - 6 q^{5} - 2052 q^{6} - 2 q^{9} + 4094 q^{10} + 680322 q^{12} - 4 q^{13} - 1533168 q^{14} - 2 q^{16} + 9329156 q^{18} - 6 q^{20} + 12211746 q^{21} - 4098 q^{22} - 89319158 q^{24} + 4960937502 q^{25} + 6144 q^{26} + 4194300 q^{28} + 289470720 q^{29} + 32688097 q^{30} + 708586 q^{33} - 2050 q^{34} - 731502418 q^{36} - 4 q^{37} - 2219597901 q^{38} - 48828124 q^{40} - 12 q^{41} - 210877804 q^{42} + 4531600317 q^{44} + 895324998 q^{45} - 4098 q^{46} + 1652757149 q^{48} - 2 q^{49} + 146484369 q^{50} - 8388607 q^{52} - 4557890371 q^{54} - 5931980232 q^{56} + 530076788 q^{57} + 4097 q^{58} - 12409318543 q^{60} - 4 q^{61} - 8 q^{64} - 1041078252 q^{66} - 52490087472 q^{68} - 5388117318 q^{69} - 4052311785 q^{70} - 69623545330 q^{72} - 4 q^{73} + 33089150787 q^{74} - 4194306 q^{76} - 53027262318 q^{77} + 38638745179 q^{78} - 53146328703 q^{80} + 14696232350 q^{81} - 2050 q^{82} - 84156752767 q^{84} - 97656254 q^{85} + 197267408361 q^{86} + 8589934593 q^{88} - 322931492340 q^{89} + 82410586919 q^{90} + 285538856784 q^{92} - 62414840370 q^{93} - 16386 q^{94} - 455036759213 q^{96} - 4 q^{97} + 47674396461 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

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