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Properties

Label 1600.2.u
Level $1600$
Weight $2$
Character orbit 1600.u
Rep. character $\chi_{1600}(321,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $232$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.u (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1008 248 760
Cusp forms 912 232 680
Eisenstein series 96 16 80

Trace form

\( 232 q + 8 q^{5} - 60 q^{9} + O(q^{10}) \) \( 232 q + 8 q^{5} - 60 q^{9} + 6 q^{13} - 14 q^{17} + 24 q^{21} - 12 q^{25} + 6 q^{29} + 6 q^{33} + 6 q^{37} - 14 q^{41} + 16 q^{45} + 168 q^{49} + 54 q^{53} - 4 q^{57} + 6 q^{61} - 18 q^{65} + 42 q^{69} + 2 q^{73} + 96 q^{77} - 36 q^{81} + 22 q^{85} - 18 q^{89} + 52 q^{93} + 34 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)