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Properties

Label 252.8.x
Level $252$
Weight $8$
Character orbit 252.x
Rep. character $\chi_{252}(41,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
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.x (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 684 112 572
Cusp forms 660 112 548
Eisenstein series 24 0 24

Trace form

\( 112 q + 83 q^{7} - 360 q^{9} + O(q^{10}) \) \( 112 q + 83 q^{7} - 360 q^{9} + 8862 q^{11} + 3732 q^{15} + 4545 q^{21} + 144078 q^{23} - 875000 q^{25} - 192036 q^{29} + 24868 q^{37} + 1579194 q^{39} + 48052 q^{43} - 179009 q^{49} + 3708198 q^{51} + 25806 q^{57} + 4841649 q^{63} + 8387904 q^{65} + 2503718 q^{67} - 3436797 q^{77} + 3834068 q^{79} - 11425356 q^{81} + 1317750 q^{85} - 854298 q^{91} + 4632888 q^{93} + 7028580 q^{95} - 682686 q^{99} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)