Properties

Label 8400.2.gc
Level $8400$
Weight $2$
Character orbit 8400.gc
Rep. character $\chi_{8400}(907,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2304$
Sturm bound $3840$

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Defining parameters

Level: \( N \) \(=\) \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8400.gc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(3840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8400, [\chi])\).

Total New Old
Modular forms 7776 2304 5472
Cusp forms 7584 2304 5280
Eisenstein series 192 0 192

Decomposition of \(S_{2}^{\mathrm{new}}(8400, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(8400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2800, [\chi])\)\(^{\oplus 2}\)