Properties

Label 1600.2.by
Level $1600$
Weight $2$
Character orbit 1600.by
Rep. character $\chi_{1600}(63,\cdot)$
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.by (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
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 2016 496 1520
Cusp forms 1824 464 1360
Eisenstein series 192 32 160

Trace form

\( 464q + 16q^{5} - 20q^{9} + O(q^{10}) \) \( 464q + 16q^{5} - 20q^{9} + 16q^{13} - 8q^{17} + 12q^{21} - 8q^{25} + 20q^{29} - 28q^{33} + 16q^{37} - 12q^{41} + 36q^{45} - 32q^{53} - 4q^{57} + 12q^{61} - 24q^{65} + 20q^{69} - 8q^{73} + 92q^{77} + 72q^{81} + 64q^{85} + 20q^{89} + 76q^{93} - 152q^{97} + O(q^{100}) \)

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

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