Newspace parameters
Level: | \( N \) | \(=\) | \( 58 = 2 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 58.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(3.42211078033\) |
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 | 7.00000 | 4.00000 | 5.00000 | −14.0000 | −2.00000 | −8.00000 | 22.0000 | −10.0000 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(29\) | \(1\) |
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 | 58.4.a.a | ✓ | 1 |
3.b | odd | 2 | 1 | 522.4.a.e | 1 | ||
4.b | odd | 2 | 1 | 464.4.a.a | 1 | ||
5.b | even | 2 | 1 | 1450.4.a.e | 1 | ||
8.b | even | 2 | 1 | 1856.4.a.a | 1 | ||
8.d | odd | 2 | 1 | 1856.4.a.d | 1 | ||
29.b | even | 2 | 1 | 1682.4.a.b | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
58.4.a.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
464.4.a.a | 1 | 4.b | odd | 2 | 1 | ||
522.4.a.e | 1 | 3.b | odd | 2 | 1 | ||
1450.4.a.e | 1 | 5.b | even | 2 | 1 | ||
1682.4.a.b | 1 | 29.b | even | 2 | 1 | ||
1856.4.a.a | 1 | 8.b | even | 2 | 1 | ||
1856.4.a.d | 1 | 8.d | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} - 7 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(58))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T + 2 \)
$3$
\( T - 7 \)
$5$
\( T - 5 \)
$7$
\( T + 2 \)
$11$
\( T - 37 \)
$13$
\( T - 27 \)
$17$
\( T - 24 \)
$19$
\( T + 88 \)
$23$
\( T + 28 \)
$29$
\( T + 29 \)
$31$
\( T + 143 \)
$37$
\( T + 360 \)
$41$
\( T - 386 \)
$43$
\( T - 381 \)
$47$
\( T + 103 \)
$53$
\( T + 431 \)
$59$
\( T - 288 \)
$61$
\( T + 840 \)
$67$
\( T + 180 \)
$71$
\( T - 706 \)
$73$
\( T - 716 \)
$79$
\( T - 931 \)
$83$
\( T - 1188 \)
$89$
\( T + 642 \)
$97$
\( T - 486 \)
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