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Properties

Label 252.8.bi
Level $252$
Weight $8$
Character orbit 252.bi
Rep. character $\chi_{252}(139,\cdot)$
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.bi (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

\( 664 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 664 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} + 14238 q^{14} - 2 q^{16} - 21178 q^{18} + 5542 q^{21} - 514 q^{22} + 4937496 q^{25} - 32772 q^{28} - 128028 q^{29} + 52232 q^{30} + 965488 q^{32} - 2038286 q^{36} - 16 q^{37} + 2696692 q^{42} - 165380 q^{44} - 520 q^{46} - 2 q^{49} + 532940 q^{50} - 16 q^{53} + 2075484 q^{56} - 911208 q^{57} + 510 q^{58} - 387928 q^{60} - 8 q^{64} - 2732452 q^{65} - 979666 q^{70} + 4524716 q^{72} + 18216136 q^{74} - 319558 q^{77} - 1943424 q^{78} + 20898256 q^{81} - 19749346 q^{84} + 312496 q^{85} + 20043124 q^{86} + 4194302 q^{88} + 48667238 q^{92} - 11751948 q^{93} + 64341964 q^{98} + O(q^{100}) \)

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.