Newspace parameters
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(4.13013370040\) |
Analytic rank: | \(0\) |
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 |
|
−2.00000 | −8.00000 | 4.00000 | −5.00000 | 16.0000 | −7.00000 | −8.00000 | 37.0000 | 10.0000 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(5\) | \(1\) |
\(7\) | \(1\) |
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 | 70.4.a.a | ✓ | 1 |
3.b | odd | 2 | 1 | 630.4.a.s | 1 | ||
4.b | odd | 2 | 1 | 560.4.a.q | 1 | ||
5.b | even | 2 | 1 | 350.4.a.v | 1 | ||
5.c | odd | 4 | 2 | 350.4.c.n | 2 | ||
7.b | odd | 2 | 1 | 490.4.a.g | 1 | ||
7.c | even | 3 | 2 | 490.4.e.r | 2 | ||
7.d | odd | 6 | 2 | 490.4.e.j | 2 | ||
8.b | even | 2 | 1 | 2240.4.a.bi | 1 | ||
8.d | odd | 2 | 1 | 2240.4.a.d | 1 | ||
35.c | odd | 2 | 1 | 2450.4.a.x | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
70.4.a.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
350.4.a.v | 1 | 5.b | even | 2 | 1 | ||
350.4.c.n | 2 | 5.c | odd | 4 | 2 | ||
490.4.a.g | 1 | 7.b | odd | 2 | 1 | ||
490.4.e.j | 2 | 7.d | odd | 6 | 2 | ||
490.4.e.r | 2 | 7.c | even | 3 | 2 | ||
560.4.a.q | 1 | 4.b | odd | 2 | 1 | ||
630.4.a.s | 1 | 3.b | odd | 2 | 1 | ||
2240.4.a.d | 1 | 8.d | odd | 2 | 1 | ||
2240.4.a.bi | 1 | 8.b | even | 2 | 1 | ||
2450.4.a.x | 1 | 35.c | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 8 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(70))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T + 2 \)
$3$
\( T + 8 \)
$5$
\( T + 5 \)
$7$
\( T + 7 \)
$11$
\( T - 68 \)
$13$
\( T - 34 \)
$17$
\( T - 74 \)
$19$
\( T + 128 \)
$23$
\( T + 80 \)
$29$
\( T - 286 \)
$31$
\( T + 24 \)
$37$
\( T - 294 \)
$41$
\( T - 66 \)
$43$
\( T + 124 \)
$47$
\( T - 312 \)
$53$
\( T + 34 \)
$59$
\( T - 168 \)
$61$
\( T - 170 \)
$67$
\( T - 564 \)
$71$
\( T - 616 \)
$73$
\( T - 250 \)
$79$
\( T + 944 \)
$83$
\( T - 672 \)
$89$
\( T + 1430 \)
$97$
\( T + 1270 \)
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