Properties

Label 5600.2.w
Level $5600$
Weight $2$
Character orbit 5600.w
Rep. character $\chi_{5600}(657,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $280$
Sturm bound $1920$

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Defining parameters

Level: \( N \) \(=\) \( 5600 = 2^{5} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5600.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(i)\)
Sturm bound: \(1920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5600, [\chi])\).

Total New Old
Modular forms 2016 296 1720
Cusp forms 1824 280 1544
Eisenstein series 192 16 176

Decomposition of \(S_{2}^{\mathrm{new}}(5600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(5600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1400, [\chi])\)\(^{\oplus 3}\)