Newspace parameters
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(123.495541256\) |
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 | −30.0000 | 16.0000 | 25.0000 | 120.000 | −49.0000 | −64.0000 | 657.000 | −100.000 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(5\) | \(-1\) |
\(7\) | \(1\) |
\(11\) | \(-1\) |
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 | 770.6.a.a | ✓ | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
770.6.a.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 30 \)
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(770))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T + 4 \)
$3$
\( T + 30 \)
$5$
\( T - 25 \)
$7$
\( T + 49 \)
$11$
\( T - 121 \)
$13$
\( T - 408 \)
$17$
\( T + 252 \)
$19$
\( T + 372 \)
$23$
\( T + 2314 \)
$29$
\( T - 3266 \)
$31$
\( T + 1808 \)
$37$
\( T + 1542 \)
$41$
\( T + 10570 \)
$43$
\( T + 6564 \)
$47$
\( T - 1722 \)
$53$
\( T + 15006 \)
$59$
\( T - 49148 \)
$61$
\( T - 5666 \)
$67$
\( T + 26318 \)
$71$
\( T + 1612 \)
$73$
\( T - 63332 \)
$79$
\( T + 40360 \)
$83$
\( T - 63972 \)
$89$
\( T - 85830 \)
$97$
\( T - 13526 \)
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