Properties

Label 1600.2.bu
Level $1600$
Weight $2$
Character orbit 1600.bu
Rep. character $\chi_{1600}(81,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $464$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.bu (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1984 496 1488
Cusp forms 1856 464 1392
Eisenstein series 128 32 96

Trace form

\( 464q + 6q^{3} - 8q^{5} + O(q^{10}) \) \( 464q + 6q^{3} - 8q^{5} + 6q^{11} - 6q^{13} + 16q^{15} - 12q^{17} + 6q^{19} + 12q^{21} + 18q^{27} - 6q^{29} - 12q^{31} - 12q^{33} - 44q^{35} - 6q^{37} + 48q^{43} - 12q^{45} + 12q^{47} - 400q^{49} + 4q^{51} - 6q^{53} + 6q^{59} - 6q^{61} - 72q^{63} + 16q^{65} - 30q^{67} - 18q^{69} + 26q^{75} + 36q^{77} + 52q^{79} + 72q^{81} + 46q^{83} + 2q^{85} - 36q^{91} - 4q^{93} + 40q^{95} - 12q^{97} + 40q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)