Newspace parameters
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(15.3668636112\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
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 | 306.000 | 0 | −3125.00 | 0 | −32074.0 | 0 | −83511.0 | 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 | 20.12.a.a | ✓ | 1 |
3.b | odd | 2 | 1 | 180.12.a.a | 1 | ||
4.b | odd | 2 | 1 | 80.12.a.c | 1 | ||
5.b | even | 2 | 1 | 100.12.a.a | 1 | ||
5.c | odd | 4 | 2 | 100.12.c.b | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
20.12.a.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
80.12.a.c | 1 | 4.b | odd | 2 | 1 | ||
100.12.a.a | 1 | 5.b | even | 2 | 1 | ||
100.12.c.b | 2 | 5.c | odd | 4 | 2 | ||
180.12.a.a | 1 | 3.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} - 306 \)
acting on \(S_{12}^{\mathrm{new}}(\Gamma_0(20))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T - 306 \)
$5$
\( T + 3125 \)
$7$
\( T + 32074 \)
$11$
\( T + 5280 \)
$13$
\( T - 227834 \)
$17$
\( T + 5097318 \)
$19$
\( T + 16279036 \)
$23$
\( T + 33055038 \)
$29$
\( T + 2112786 \)
$31$
\( T - 91337396 \)
$37$
\( T + 109132054 \)
$41$
\( T - 1202079126 \)
$43$
\( T - 1112512490 \)
$47$
\( T - 507908142 \)
$53$
\( T + 1900361502 \)
$59$
\( T - 2802066708 \)
$61$
\( T + 9660996838 \)
$67$
\( T - 8370234446 \)
$71$
\( T + 12173973252 \)
$73$
\( T - 18053518034 \)
$79$
\( T - 22759013912 \)
$83$
\( T - 65367228042 \)
$89$
\( T + 13526251734 \)
$97$
\( T + 155553294334 \)
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