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Properties

Label 3200.2.bt
Level $3200$
Weight $2$
Character orbit 3200.bt
Rep. character $\chi_{3200}(223,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $928$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3200.bt (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3200, [\chi])\).

Total New Old
Modular forms 3968 992 2976
Cusp forms 3712 928 2784
Eisenstein series 256 64 192

Trace form

\( 928 q + 16 q^{5} - 216 q^{9} + O(q^{10}) \) \( 928 q + 16 q^{5} - 216 q^{9} + 20 q^{13} - 32 q^{17} - 48 q^{21} + 20 q^{29} - 32 q^{33} + 20 q^{37} - 16 q^{45} + 12 q^{53} + 24 q^{57} + 12 q^{61} - 32 q^{65} - 4 q^{69} + 16 q^{73} + 96 q^{77} - 192 q^{81} + 36 q^{85} - 32 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3200, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1600, [\chi])\)\(^{\oplus 2}\)