Properties

Label 800.1.bo
Level $800$
Weight $1$
Character orbit 800.bo
Rep. character $\chi_{800}(33,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $8$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 800.bo (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(800, [\chi])\).

Total New Old
Modular forms 72 8 64
Cusp forms 8 8 0
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

\( 8 q + O(q^{10}) \) \( 8 q + 2 q^{13} + 2 q^{17} + 2 q^{25} - 2 q^{37} - 2 q^{45} - 2 q^{53} - 2 q^{65} - 2 q^{73} + 2 q^{81} - 8 q^{85} - 10 q^{89} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
800.1.bo.a 800.bo 25.f $8$ $0.399$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{7}q^{5}+\zeta_{20}q^{9}+(-\zeta_{20}^{8}+\zeta_{20}^{9}+\cdots)q^{13}+\cdots\)