Properties

Label 8470.2.df
Level $8470$
Weight $2$
Character orbit 8470.df
Rep. character $\chi_{8470}(97,\cdot)$
Character field $\Q(\zeta_{220})$
Dimension $42240$
Sturm bound $3168$

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Defining parameters

Level: \( N \) \(=\) \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8470.df (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4235 \)
Character field: \(\Q(\zeta_{220})\)
Sturm bound: \(3168\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8470, [\chi])\).

Total New Old
Modular forms 127360 42240 85120
Cusp forms 126080 42240 83840
Eisenstein series 1280 0 1280

Decomposition of \(S_{2}^{\mathrm{new}}(8470, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(8470, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(4235, [\chi])\)\(^{\oplus 2}\)