Properties

Label 4000.1.cq
Level 4000
Weight 1
Character orbit cq
Rep. character \(\chi_{4000}(33,\cdot)\)
Character field \(\Q(\zeta_{100})\)
Dimension 40
Newform subspaces 1
Sturm bound 600
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 4000 = 2^{5} \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 4000.cq (of order \(100\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 125 \)
Character field: \(\Q(\zeta_{100})\)
Newform subspaces: \( 1 \)
Sturm bound: \(600\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(4000, [\chi])\).

Total New Old
Modular forms 360 40 320
Cusp forms 40 40 0
Eisenstein series 320 0 320

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 40 0 0 0

Trace form

\( 40q + O(q^{10}) \) \( 40q + 10q^{85} + 10q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(4000, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4000.1.cq.a \(40\) \(1.996\) \(\Q(\zeta_{100})\) \(D_{100}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{100}^{13}q^{5}-\zeta_{100}^{49}q^{9}+(\zeta_{100}^{2}-\zeta_{100}^{21}+\cdots)q^{13}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - T^{20} + T^{40} - T^{60} + T^{80} \)
$5$ \( 1 - T^{10} + T^{20} - T^{30} + T^{40} \)
$7$ \( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} )^{5} \)
$11$ \( ( 1 - T^{10} + T^{20} - T^{30} + T^{40} )^{2} \)
$13$ \( ( 1 - T^{5} + T^{10} - T^{15} + T^{20} )^{2}( 1 - T^{10} + T^{20} - T^{30} + T^{40} ) \)
$17$ \( ( 1 - T^{5} + T^{10} - T^{15} + T^{20} )^{2}( 1 - T^{10} + T^{20} - T^{30} + T^{40} ) \)
$19$ \( ( 1 - T^{5} + T^{10} - T^{15} + T^{20} )^{2}( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{2} \)
$23$ \( 1 - T^{20} + T^{40} - T^{60} + T^{80} \)
$29$ \( ( 1 - T^{5} + T^{10} - T^{15} + T^{20} )^{2}( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{2} \)
$31$ \( ( 1 - T^{10} + T^{20} - T^{30} + T^{40} )^{2} \)
$37$ \( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{5}( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{2} \)
$41$ \( ( 1 - T^{10} + T^{20} - T^{30} + T^{40} )^{2} \)
$43$ \( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} )^{5} \)
$47$ \( 1 - T^{20} + T^{40} - T^{60} + T^{80} \)
$53$ \( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{5}( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{2} \)
$59$ \( ( 1 - T^{5} + T^{10} - T^{15} + T^{20} )^{2}( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{2} \)
$61$ \( ( 1 - T^{10} + T^{20} - T^{30} + T^{40} )^{2} \)
$67$ \( 1 - T^{20} + T^{40} - T^{60} + T^{80} \)
$71$ \( ( 1 - T^{10} + T^{20} - T^{30} + T^{40} )^{2} \)
$73$ \( ( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{2}( 1 - T^{10} + T^{20} - T^{30} + T^{40} ) \)
$79$ \( ( 1 - T^{5} + T^{10} - T^{15} + T^{20} )^{2}( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{2} \)
$83$ \( 1 - T^{20} + T^{40} - T^{60} + T^{80} \)
$89$ \( ( 1 - T + T^{2} - T^{3} + T^{4} )^{10}( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{2} \)
$97$ \( ( 1 + T^{5} + T^{10} + T^{15} + T^{20} )^{2}( 1 - T^{10} + T^{20} - T^{30} + T^{40} ) \)
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