Newspace parameters
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(0.638803216170\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 20) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
Expression as an eta quotient
\(f(z) = \dfrac{\eta(4z)^{6}\eta(20z)^{6}}{\eta(2z)^{2}\eta(8z)^{2}\eta(10z)^{2}\eta(40z)^{2}}=q\prod_{n=1}^\infty(1 - q^{2n})^{-2}(1 - q^{4n})^{6}(1 - q^{8n})^{-2}(1 - q^{10n})^{-2}(1 - q^{20n})^{6}(1 - q^{40n})^{-2}\)
Embeddings
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Label | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.1 |
|
0 | 2.00000 | 0 | −1.00000 | 0 | −2.00000 | 0 | 1.00000 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(5\) | \(1\) |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} - 2 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(80))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T - 2 \)
$5$
\( T + 1 \)
$7$
\( T + 2 \)
$11$
\( T \)
$13$
\( T - 2 \)
$17$
\( T + 6 \)
$19$
\( T - 4 \)
$23$
\( T + 6 \)
$29$
\( T - 6 \)
$31$
\( T - 4 \)
$37$
\( T - 2 \)
$41$
\( T - 6 \)
$43$
\( T - 10 \)
$47$
\( T - 6 \)
$53$
\( T + 6 \)
$59$
\( T + 12 \)
$61$
\( T - 2 \)
$67$
\( T + 2 \)
$71$
\( T - 12 \)
$73$
\( T - 2 \)
$79$
\( T + 8 \)
$83$
\( T + 6 \)
$89$
\( T + 6 \)
$97$
\( T - 2 \)
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