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Properties

Label 1600.3.bd
Level $1600$
Weight $3$
Character orbit 1600.bd
Rep. character $\chi_{1600}(31,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $480$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1600.bd (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1600, [\chi])\).

Total New Old
Modular forms 1968 480 1488
Cusp forms 1872 480 1392
Eisenstein series 96 0 96

Trace form

\( 480 q - 360 q^{9} + O(q^{10}) \) \( 480 q - 360 q^{9} + 48 q^{17} + 72 q^{25} - 240 q^{41} - 3360 q^{49} - 72 q^{65} - 144 q^{73} - 1080 q^{81} - 360 q^{89} + 720 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1600, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)