Properties

Label 4000.1.g
Level $4000$
Weight $1$
Character orbit 4000.g
Rep. character $\chi_{4000}(751,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $600$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 4000 = 2^{5} \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 4000.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
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 72 4 68
Cusp forms 32 4 28
Eisenstein series 40 0 40

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{9} + 2q^{11} - 2q^{19} - 2q^{41} - 2q^{49} - 2q^{59} + 4q^{81} + 2q^{89} + 4q^{91} - 2q^{99} + O(q^{100}) \)

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.g.a \(4\) \(1.996\) \(\Q(i, \sqrt{5})\) \(D_{5}\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{7}-q^{9}-\beta _{2}q^{11}-\beta _{1}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(4000, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(4000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1000, [\chi])\)\(^{\oplus 3}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( ( 1 + T^{2} )^{4} \)
$5$ 1
$7$ \( 1 - T^{2} + T^{4} - T^{6} + T^{8} \)
$11$ \( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2} \)
$13$ \( 1 - T^{2} + T^{4} - T^{6} + T^{8} \)
$17$ \( ( 1 + T^{2} )^{4} \)
$19$ \( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \)
$23$ \( 1 - T^{2} + T^{4} - T^{6} + T^{8} \)
$29$ \( ( 1 - T )^{4}( 1 + T )^{4} \)
$31$ \( ( 1 - T )^{4}( 1 + T )^{4} \)
$37$ \( 1 - T^{2} + T^{4} - T^{6} + T^{8} \)
$41$ \( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \)
$43$ \( ( 1 + T^{2} )^{4} \)
$47$ \( 1 - T^{2} + T^{4} - T^{6} + T^{8} \)
$53$ \( 1 - T^{2} + T^{4} - T^{6} + T^{8} \)
$59$ \( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \)
$61$ \( ( 1 - T )^{4}( 1 + T )^{4} \)
$67$ \( ( 1 + T^{2} )^{4} \)
$71$ \( ( 1 - T )^{4}( 1 + T )^{4} \)
$73$ \( ( 1 + T^{2} )^{4} \)
$79$ \( ( 1 - T )^{4}( 1 + T )^{4} \)
$83$ \( ( 1 + T^{2} )^{4} \)
$89$ \( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2} \)
$97$ \( ( 1 + T^{2} )^{4} \)
show more
show less