Newspace parameters
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(1.60383819813\) |
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 |
|
−4.00000 | −26.0000 | 16.0000 | −25.0000 | 104.000 | −22.0000 | −64.0000 | 433.000 | 100.000 | |||||||||||||||||||||
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 | 10.6.a.a | ✓ | 1 |
3.b | odd | 2 | 1 | 90.6.a.f | 1 | ||
4.b | odd | 2 | 1 | 80.6.a.h | 1 | ||
5.b | even | 2 | 1 | 50.6.a.g | 1 | ||
5.c | odd | 4 | 2 | 50.6.b.d | 2 | ||
7.b | odd | 2 | 1 | 490.6.a.j | 1 | ||
8.b | even | 2 | 1 | 320.6.a.p | 1 | ||
8.d | odd | 2 | 1 | 320.6.a.a | 1 | ||
12.b | even | 2 | 1 | 720.6.a.r | 1 | ||
15.d | odd | 2 | 1 | 450.6.a.h | 1 | ||
15.e | even | 4 | 2 | 450.6.c.o | 2 | ||
20.d | odd | 2 | 1 | 400.6.a.a | 1 | ||
20.e | even | 4 | 2 | 400.6.c.a | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
10.6.a.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
50.6.a.g | 1 | 5.b | even | 2 | 1 | ||
50.6.b.d | 2 | 5.c | odd | 4 | 2 | ||
80.6.a.h | 1 | 4.b | odd | 2 | 1 | ||
90.6.a.f | 1 | 3.b | odd | 2 | 1 | ||
320.6.a.a | 1 | 8.d | odd | 2 | 1 | ||
320.6.a.p | 1 | 8.b | even | 2 | 1 | ||
400.6.a.a | 1 | 20.d | odd | 2 | 1 | ||
400.6.c.a | 2 | 20.e | even | 4 | 2 | ||
450.6.a.h | 1 | 15.d | odd | 2 | 1 | ||
450.6.c.o | 2 | 15.e | even | 4 | 2 | ||
490.6.a.j | 1 | 7.b | odd | 2 | 1 | ||
720.6.a.r | 1 | 12.b | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 26 \)
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(10))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T + 4 \)
$3$
\( T + 26 \)
$5$
\( T + 25 \)
$7$
\( T + 22 \)
$11$
\( T + 768 \)
$13$
\( T + 46 \)
$17$
\( T - 378 \)
$19$
\( T - 1100 \)
$23$
\( T + 1986 \)
$29$
\( T + 5610 \)
$31$
\( T + 3988 \)
$37$
\( T + 142 \)
$41$
\( T - 1542 \)
$43$
\( T + 5026 \)
$47$
\( T - 24738 \)
$53$
\( T + 14166 \)
$59$
\( T - 28380 \)
$61$
\( T - 5522 \)
$67$
\( T + 24742 \)
$71$
\( T - 42372 \)
$73$
\( T + 52126 \)
$79$
\( T + 39640 \)
$83$
\( T + 59826 \)
$89$
\( T - 57690 \)
$97$
\( T + 144382 \)
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