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Properties

Label 252.8.ba
Level $252$
Weight $8$
Character orbit 252.ba
Rep. character $\chi_{252}(155,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $504$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
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 680 504 176
Cusp forms 664 504 160
Eisenstein series 16 0 16

Trace form

\( 504 q - 174 q^{6} + 2236 q^{9} + O(q^{10}) \) \( 504 q - 174 q^{6} + 2236 q^{9} + 24036 q^{12} + 165458 q^{18} - 261618 q^{20} + 352606 q^{24} + 3937500 q^{25} + 807124 q^{30} + 308910 q^{32} + 625228 q^{33} + 390444 q^{34} + 643556 q^{36} - 799500 q^{40} - 4509060 q^{41} + 1159340 q^{42} + 1105464 q^{45} - 2164488 q^{46} + 7418516 q^{48} + 29647548 q^{49} + 742638 q^{50} + 2243574 q^{52} - 6848398 q^{54} + 2555012 q^{57} - 2589534 q^{58} - 6789484 q^{60} - 5642556 q^{64} + 6322344 q^{65} + 18715482 q^{66} - 7140666 q^{68} + 1874184 q^{69} + 13321658 q^{72} + 6405528 q^{73} + 9008496 q^{74} - 7301796 q^{76} + 12776980 q^{78} + 22575524 q^{81} - 3564252 q^{82} + 8273846 q^{84} - 30887430 q^{86} - 15250728 q^{88} + 44060120 q^{90} + 40830582 q^{92} + 75417312 q^{93} - 3218754 q^{94} + 44409232 q^{96} - 10592724 q^{97} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)