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Properties

Label 252.8.be
Level $252$
Weight $8$
Character orbit 252.be
Rep. character $\chi_{252}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $224$
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.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
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 688 224 464
Cusp forms 656 224 432
Eisenstein series 32 0 32

Trace form

\( 224 q + O(q^{10}) \) \( 224 q + 14128 q^{13} - 10556 q^{16} + 117856 q^{22} + 1729512 q^{25} + 271108 q^{28} + 909200 q^{34} - 634024 q^{37} - 311188 q^{40} - 1210824 q^{46} + 516752 q^{49} - 3359044 q^{52} + 1529964 q^{58} + 614864 q^{61} - 13476552 q^{64} - 17640108 q^{70} - 13631864 q^{73} + 39652776 q^{76} - 11193604 q^{82} + 14318752 q^{85} + 11242892 q^{88} + 55212756 q^{94} + 146755888 q^{97} + O(q^{100}) \)

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

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