Properties

Label 800.1.bh
Level 800
Weight 1
Character orbit bh
Rep. character \(\chi_{800}(31,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 8
Newforms 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.bh (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
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 56 8 48
Cusp forms 24 8 16
Eisenstein series 32 0 32

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

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

Trace form

\(8q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 8q^{93} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(800, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
800.1.bh.a \(8\) \(0.399\) \(\Q(\zeta_{20})\) \(A_{5}\) None None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{4}q^{5}+(\zeta_{20}+\zeta_{20}^{9}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)