Properties

Label 3200.1.bd
Level $3200$
Weight $1$
Character orbit 3200.bd
Rep. character $\chi_{3200}(191,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $8$
Newform subspaces $2$
Sturm bound $480$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3200.bd (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(480\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3200, [\chi])\).

Total New Old
Modular forms 104 8 96
Cusp forms 40 8 32
Eisenstein series 64 0 64

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 2 q^{9} + O(q^{10}) \) \( 8 q + 2 q^{9} + 4 q^{17} - 2 q^{25} - 4 q^{41} + 8 q^{49} + 10 q^{65} + 4 q^{73} - 2 q^{81} - 6 q^{89} + 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3200, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3200.1.bd.a 3200.bd 200.n $4$ $1.597$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+\zeta_{10}^{4}q^{5}-\zeta_{10}^{2}q^{9}+(-\zeta_{10}+\zeta_{10}^{3}+\cdots)q^{13}+\cdots\)
3200.1.bd.b 3200.bd 200.n $4$ $1.597$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q-\zeta_{10}^{4}q^{5}-\zeta_{10}^{2}q^{9}+(\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3200, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3200, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(1600, [\chi])\)\(^{\oplus 2}\)