Properties

Label 1600.2.bg
Level $1600$
Weight $2$
Character orbit 1600.bg
Rep. character $\chi_{1600}(129,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $232$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.bg (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
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 248 760
Cusp forms 912 232 680
Eisenstein series 96 16 80

Trace form

\( 232q + 8q^{5} + 48q^{9} + O(q^{10}) \) \( 232q + 8q^{5} + 48q^{9} + 10q^{13} - 10q^{17} - 12q^{21} - 12q^{25} + 6q^{29} - 10q^{33} + 10q^{37} + 2q^{41} - 20q^{45} - 200q^{49} + 10q^{53} + 6q^{61} - 6q^{65} + 66q^{69} - 10q^{73} - 60q^{77} - 60q^{81} + 42q^{85} - 18q^{89} + 70q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)