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Properties

Label 252.8.n
Level $252$
Weight $8$
Character orbit 252.n
Rep. character $\chi_{252}(31,\cdot)$
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.n (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

\( 664 q + q^{2} + q^{4} - 384 q^{6} - 8 q^{8} - 2 q^{9} + O(q^{10}) \) \( 664 q + q^{2} + q^{4} - 384 q^{6} - 8 q^{8} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 29247 q^{14} + q^{16} - 12 q^{17} - 21175 q^{18} + 98304 q^{20} - 11096 q^{21} + 254 q^{22} + 6558 q^{24} - 9875004 q^{25} - 390 q^{26} + 16380 q^{28} + 64008 q^{29} - 352738 q^{30} - 637199 q^{32} - 6 q^{33} + 384 q^{34} + 256102 q^{36} - 4 q^{37} + 1249597 q^{42} + 7807 q^{44} + 1513494 q^{45} + 254 q^{46} - 6561 q^{48} - 2 q^{49} + 297797 q^{50} - 4 q^{53} + 7169466 q^{54} - 494976 q^{56} - 884964 q^{57} + 510 q^{58} + 379184 q^{60} - 6 q^{61} - 8 q^{64} - 1794946 q^{65} + 839805 q^{66} + 13122 q^{69} - 511300 q^{70} - 3568951 q^{72} - 12 q^{73} + 24044866 q^{74} - 49152 q^{76} + 9562958 q^{77} + 4540281 q^{78} - 11290053 q^{80} - 10449134 q^{81} - 390 q^{82} - 21698347 q^{84} - 156254 q^{85} - 10844306 q^{86} + 4194302 q^{88} - 28554192 q^{89} + 12135009 q^{90} + 11290652 q^{92} - 11751942 q^{93} - 3 q^{94} + 42325866 q^{96} - 78087749 q^{98} + O(q^{100}) \)

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.