Properties

Label 800.1.g
Level 800
Weight 1
Character orbit g
Rep. character \(\chi_{800}(751,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 2 \)
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 32 5 27
Cusp forms 8 2 6
Eisenstein series 24 3 21

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q + O(q^{10}) \) \( 2q + 2q^{11} + 2q^{19} - 2q^{41} + 2q^{49} - 2q^{51} - 4q^{59} - 2q^{81} - 2q^{89} + O(q^{100}) \)

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.g.a \(1\) \(0.399\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{11}+q^{17}+q^{19}+q^{27}+\cdots\)
800.1.g.b \(1\) \(0.399\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{11}-q^{17}+q^{19}-q^{27}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)