Properties

Label 800.1.g
Level $800$
Weight $1$
Character orbit 800.g
Rep. character $\chi_{800}(751,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

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.g.a 800.g 8.d $1$ $0.399$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{11}+q^{17}+q^{19}+q^{27}+\cdots\)
800.1.g.b 800.g 8.d $1$ $0.399$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-2}) \) 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

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