Newspace parameters
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(114.154804080\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
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 | 918.000 | 0 | −78125.0 | 0 | 953554. | 0 | −1.35062e7 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(5\) | \(1\) |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 80.16.a.a | 1 | |
4.b | odd | 2 | 1 | 10.16.a.b | ✓ | 1 | |
12.b | even | 2 | 1 | 90.16.a.h | 1 | ||
20.d | odd | 2 | 1 | 50.16.a.c | 1 | ||
20.e | even | 4 | 2 | 50.16.b.c | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
10.16.a.b | ✓ | 1 | 4.b | odd | 2 | 1 | |
50.16.a.c | 1 | 20.d | odd | 2 | 1 | ||
50.16.b.c | 2 | 20.e | even | 4 | 2 | ||
80.16.a.a | 1 | 1.a | even | 1 | 1 | trivial | |
90.16.a.h | 1 | 12.b | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} - 918 \)
acting on \(S_{16}^{\mathrm{new}}(\Gamma_0(80))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T - 918 \)
$5$
\( T + 78125 \)
$7$
\( T - 953554 \)
$11$
\( T + 17783232 \)
$13$
\( T - 140533322 \)
$17$
\( T - 2998870746 \)
$19$
\( T + 3255852500 \)
$23$
\( T + 6774812202 \)
$29$
\( T + 7340322690 \)
$31$
\( T - 115428411388 \)
$37$
\( T - 150300986906 \)
$41$
\( T - 1841603525142 \)
$43$
\( T + 1510018315682 \)
$47$
\( T + 6093750843366 \)
$53$
\( T + 8267412829038 \)
$59$
\( T - 23516883061980 \)
$61$
\( T + 3135369104278 \)
$67$
\( T - 36030983954794 \)
$71$
\( T + 52169735384172 \)
$73$
\( T - 69977143684082 \)
$79$
\( T - 135317670906760 \)
$83$
\( T + 427456158822882 \)
$89$
\( T + 446581617299190 \)
$97$
\( T - 181247411845826 \)
show more
show less