Properties

Label 1600.2.cb
Level $1600$
Weight $2$
Character orbit 1600.cb
Rep. character $\chi_{1600}(209,\cdot)$
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.cb (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

\( 464q + 10q^{3} - 8q^{5} + O(q^{10}) \) \( 464q + 10q^{3} - 8q^{5} + 6q^{11} - 10q^{13} + 16q^{15} - 20q^{17} + 6q^{19} - 24q^{21} + 10q^{27} - 6q^{29} + 36q^{31} - 20q^{33} + 36q^{35} - 10q^{37} - 24q^{45} + 20q^{47} + 336q^{49} + 28q^{51} - 10q^{53} + 6q^{59} - 6q^{61} + 160q^{63} - 48q^{65} + 70q^{67} + 6q^{69} + 46q^{75} - 80q^{77} + 52q^{79} + 72q^{81} + 10q^{83} - 18q^{85} + 48q^{91} + 40q^{95} - 20q^{97} + 64q^{99} + O(q^{100}) \)

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

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