Properties

Label 800.1.p
Level 800
Weight 1
Character orbit p
Rep. character \(\chi_{800}(193,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 6
Newforms 3
Sturm bound 120
Trace bound 3

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Defining parameters

Level: \( N \) = \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 800.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(3\)

Dimensions

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

Total New Old
Modular forms 58 6 52
Cusp forms 10 6 4
Eisenstein series 48 0 48

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6q + O(q^{10}) \) \( 6q + 2q^{13} + 2q^{17} - 8q^{21} - 2q^{37} - 2q^{53} - 2q^{73} + 2q^{81} - 2q^{97} + O(q^{100}) \)

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.p.a \(2\) \(0.399\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(2\) \(q+(-1+i)q^{3}+(1+i)q^{7}-iq^{9}-q^{21}+\cdots\)
800.1.p.b \(2\) \(0.399\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{9}+(1-i)q^{13}+(1+i)q^{17}+(-1+\cdots)q^{37}+\cdots\)
800.1.p.c \(2\) \(0.399\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(-2\) \(q+(1-i)q^{3}+(-1-i)q^{7}-iq^{9}-q^{21}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)