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Properties

Label 252.8.bb
Level $252$
Weight $8$
Character orbit 252.bb
Rep. character $\chi_{252}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $664$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 252.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(252, [\chi])\).

Total New Old
Modular forms 680 680 0
Cusp forms 664 664 0
Eisenstein series 16 16 0

Trace form

\( 664 q - 2 q^{4} - 6 q^{5} - 132 q^{6} - 2 q^{9} + O(q^{10}) \) \( 664 q - 2 q^{4} - 6 q^{5} - 132 q^{6} - 2 q^{9} + 254 q^{10} + 13362 q^{12} - 4 q^{13} - 43488 q^{14} - 2 q^{16} - 10204 q^{18} - 6 q^{20} - 5550 q^{21} - 258 q^{22} + 147322 q^{24} + 4937502 q^{25} + 384 q^{26} + 16380 q^{28} - 192048 q^{29} + 56737 q^{30} + 8746 q^{33} - 130 q^{34} - 1306258 q^{36} - 4 q^{37} - 254061 q^{38} - 78124 q^{40} - 12 q^{41} - 598588 q^{42} + 173181 q^{44} - 817002 q^{45} - 258 q^{46} - 4375603 q^{48} - 2 q^{49} + 234369 q^{50} - 32767 q^{52} + 2612381 q^{54} - 2470632 q^{56} + 884948 q^{57} + 257 q^{58} - 6626383 q^{60} - 4 q^{61} - 8 q^{64} + 7630116 q^{66} + 1493088 q^{68} + 108858 q^{69} - 1803465 q^{70} + 9936062 q^{72} - 4 q^{73} - 5827197 q^{74} - 16386 q^{76} - 8923854 q^{77} - 11000837 q^{78} + 10821297 q^{80} + 18056990 q^{81} - 130 q^{82} - 6881503 q^{84} - 156254 q^{85} - 45509175 q^{86} + 2097153 q^{88} - 28554180 q^{89} + 31882199 q^{90} - 37474896 q^{92} + 5897838 q^{93} - 1026 q^{94} - 50753165 q^{96} - 4 q^{97} - 23538003 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

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