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Properties

Label 3200.2.j
Level $3200$
Weight $2$
Character orbit 3200.j
Rep. character $\chi_{3200}(543,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $136$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3200.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1056 152 904
Cusp forms 864 136 728
Eisenstein series 192 16 176

Trace form

\( 136 q - 120 q^{9} + O(q^{10}) \) \( 136 q - 120 q^{9} - 8 q^{13} + 8 q^{17} + 8 q^{21} + 8 q^{33} - 8 q^{37} - 24 q^{57} + 72 q^{61} + 40 q^{69} - 16 q^{73} + 56 q^{81} + 16 q^{93} + 8 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)