Properties

Label 3200.1.bz
Level $3200$
Weight $1$
Character orbit 3200.bz
Rep. character $\chi_{3200}(577,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $16$
Newform subspaces $2$
Sturm bound $480$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3200.bz (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(480\)
Trace bound: \(13\)

Dimensions

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

Total New Old
Modular forms 144 16 128
Cusp forms 16 16 0
Eisenstein series 128 0 128

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q + O(q^{10}) \) \( 16 q - 4 q^{17} + 4 q^{25} + 4 q^{65} + 4 q^{73} + 4 q^{81} + 20 q^{89} + 4 q^{97} + O(q^{100}) \)

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.bz.a 3200.bz 200.x $8$ $1.597$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{5}-\zeta_{20}^{7}q^{9}+(\zeta_{20}^{3}-\zeta_{20}^{6}+\cdots)q^{13}+\cdots\)
3200.1.bz.b 3200.bz 200.x $8$ $1.597$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{9}q^{5}-\zeta_{20}^{7}q^{9}+(-\zeta_{20}^{3}+\zeta_{20}^{6}+\cdots)q^{13}+\cdots\)