Properties

Label 8712.2.bf
Level $8712$
Weight $2$
Character orbit 8712.bf
Rep. character $\chi_{8712}(5081,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $648$
Sturm bound $3168$

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Defining parameters

Level: \( N \) \(=\) \( 8712 = 2^{3} \cdot 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8712.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(3168\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8712, [\chi])\).

Total New Old
Modular forms 3264 648 2616
Cusp forms 3072 648 2424
Eisenstein series 192 0 192

Decomposition of \(S_{2}^{\mathrm{new}}(8712, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(8712, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8712, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1089, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2178, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4356, [\chi])\)\(^{\oplus 2}\)