Properties

Label 1600.2.be
Level $1600$
Weight $2$
Character orbit 1600.be
Rep. character $\chi_{1600}(289,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $240$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.be (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1600, [\chi])\).

Total New Old
Modular forms 1008 240 768
Cusp forms 912 240 672
Eisenstein series 96 0 96

Trace form

\( 240q - 60q^{9} + O(q^{10}) \) \( 240q - 60q^{9} - 12q^{25} + 24q^{41} - 240q^{49} - 36q^{65} - 60q^{81} - 36q^{89} + 240q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)