Properties

Label 5600.2.h
Level $5600$
Weight $2$
Character orbit 5600.h
Rep. character $\chi_{5600}(2351,\cdot)$
Character field $\Q$
Dimension $146$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Sturm bound: \(1920\)

Dimensions

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

Total New Old
Modular forms 1008 158 850
Cusp forms 912 146 766
Eisenstein series 96 12 84

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

\( S_{2}^{\mathrm{old}}(5600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1400, [\chi])\)\(^{\oplus 3}\)