Properties

Label 2008.1.bd
Level 2008
Weight 1
Character orbit bd
Rep. character \(\chi_{2008}(3,\cdot)\)
Character field \(\Q(\zeta_{250})\)
Dimension 100
Newform subspaces 1
Sturm bound 252
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 2008 = 2^{3} \cdot 251 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2008.bd (of order \(250\) and degree \(100\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2008 \)
Character field: \(\Q(\zeta_{250})\)
Newform subspaces: \( 1 \)
Sturm bound: \(252\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2008, [\chi])\).

Total New Old
Modular forms 300 300 0
Cusp forms 100 100 0
Eisenstein series 200 200 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 100 0 0 0

Trace form

\( 100q + O(q^{10}) \) \( 100q - 25q^{22} - 25q^{32} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2008, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2008.1.bd.a \(100\) \(1.002\) \(\Q(\zeta_{250})\) \(D_{125}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{250}^{35}q^{2}+(\zeta_{250}^{14}-\zeta_{250}^{53})q^{3}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5} \)
$3$ \( ( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2} \)
$5$ \( ( 1 - T^{5} + T^{10} - T^{15} + T^{20} )^{5}( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5} \)
$7$ \( ( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$11$ \( ( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5}( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$13$ \( ( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$17$ \( ( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2} \)
$19$ \( ( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2} \)
$23$ \( ( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$29$ \( ( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$31$ \( ( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$37$ \( ( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$41$ \( ( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2} \)
$43$ \( ( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2} \)
$47$ \( ( 1 - T^{5} + T^{10} - T^{15} + T^{20} )^{5}( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5} \)
$53$ \( ( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$59$ \( ( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5}( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$61$ \( ( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$67$ \( ( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2} \)
$71$ \( ( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$73$ \( ( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2} \)
$79$ \( ( 1 - T^{25} + T^{50} - T^{75} + T^{100} )( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$83$ \( ( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{5}( 1 + T^{25} + T^{50} + T^{75} + T^{100} ) \)
$89$ \( ( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2} \)
$97$ \( ( 1 + T^{25} + T^{50} + T^{75} + T^{100} )^{2} \)
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