↑

Properties

Label 1600.3.bf
Level $1600$
Weight $3$
Character orbit 1600.bf
Rep. character $\chi_{1600}(319,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $472$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1600.bf (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
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 488 1480
Cusp forms 1872 472 1400
Eisenstein series 96 16 80

Trace form

\( 472 q + 8 q^{5} - 348 q^{9} + O(q^{10}) \) \( 472 q + 8 q^{5} - 348 q^{9} + 10 q^{13} - 10 q^{17} + 60 q^{21} + 16 q^{25} + 6 q^{29} - 10 q^{33} + 10 q^{37} + 74 q^{41} - 12 q^{45} + 2952 q^{49} + 10 q^{53} + 6 q^{61} + 30 q^{65} - 510 q^{69} - 10 q^{73} + 500 q^{77} - 888 q^{81} + 202 q^{85} - 126 q^{89} + 150 q^{97} + O(q^{100}) \)

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

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