Properties

Label 8470.2.bh
Level $8470$
Weight $2$
Character orbit 8470.bh
Rep. character $\chi_{8470}(81,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $2304$
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.bh (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(3168\)

Dimensions

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

Total New Old
Modular forms 13056 2304 10752
Cusp forms 12288 2304 9984
Eisenstein series 768 0 768

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

\( S_{2}^{\mathrm{old}}(8470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(770, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(847, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1694, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4235, [\chi])\)\(^{\oplus 2}\)