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Properties

Label 252.8.bf
Level $252$
Weight $8$
Character orbit 252.bf
Rep. character $\chi_{252}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $276$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
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 688 284 404
Cusp forms 656 276 380
Eisenstein series 32 8 24

Trace form

\( 276 q - 6 q^{2} - 92 q^{4} + 6 q^{5} + 432 q^{8} + O(q^{10}) \) \( 276 q - 6 q^{2} - 92 q^{4} + 6 q^{5} + 432 q^{8} + 9708 q^{10} - 2878 q^{14} + 13268 q^{16} + 6 q^{17} + 144936 q^{22} + 2041492 q^{25} + 204354 q^{26} - 187156 q^{28} - 231392 q^{29} - 157796 q^{32} - 98566 q^{37} - 102474 q^{38} + 1403592 q^{40} - 413580 q^{44} - 837080 q^{46} - 782452 q^{49} - 3562908 q^{50} + 4278924 q^{52} - 565266 q^{53} - 893816 q^{56} + 783968 q^{58} - 2737578 q^{61} - 4177880 q^{64} - 2305196 q^{65} - 236088 q^{68} - 11570260 q^{70} - 5701794 q^{73} + 7101074 q^{74} + 545322 q^{77} + 1881024 q^{80} - 12512112 q^{82} + 17462812 q^{85} + 13281058 q^{86} + 11374288 q^{88} - 28554174 q^{89} + 50008104 q^{92} - 4736640 q^{94} - 43935644 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{8}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)