Properties

Label 800.1.e
Level 800
Weight 1
Character orbit e
Rep. character \(\chi_{800}(399,\cdot)\)
Character field \(\Q\)
Dimension 2
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 40 \)
Character field: \(\Q\)
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 32 4 28
Cusp forms 8 2 6
Eisenstein series 24 2 22

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 newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
800.1.e.a \(2\) \(0.399\) \(\Q(\sqrt{-1}) \) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+q^{11}-iq^{17}-q^{19}-iq^{27}+\cdots\)

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

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( \)
$3$ \( 1 - T^{2} + T^{4} \)
$5$ \( \)
$7$ \( ( 1 + T^{2} )^{2} \)
$11$ \( ( 1 - T + T^{2} )^{2} \)
$13$ \( ( 1 + T^{2} )^{2} \)
$17$ \( 1 - T^{2} + T^{4} \)
$19$ \( ( 1 + T + T^{2} )^{2} \)
$23$ \( ( 1 + T^{2} )^{2} \)
$29$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$31$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$37$ \( ( 1 + T^{2} )^{2} \)
$41$ \( ( 1 + T + T^{2} )^{2} \)
$43$ \( ( 1 + T^{2} )^{2} \)
$47$ \( ( 1 + T^{2} )^{2} \)
$53$ \( ( 1 + T^{2} )^{2} \)
$59$ \( ( 1 - T )^{4} \)
$61$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$67$ \( 1 - T^{2} + T^{4} \)
$71$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$73$ \( 1 - T^{2} + T^{4} \)
$79$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$83$ \( 1 - T^{2} + T^{4} \)
$89$ \( ( 1 - T + T^{2} )^{2} \)
$97$ \( ( 1 + T^{2} )^{2} \)
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