Newspace parameters
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(64.8945153566\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
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 |
|
16.0000 | 0 | 256.000 | 2290.00 | 0 | −2401.00 | 4096.00 | 0 | 36640.0 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(3\) | \(-1\) |
\(7\) | \(1\) |
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 | 126.10.a.h | 1 | |
3.b | odd | 2 | 1 | 42.10.a.c | ✓ | 1 | |
12.b | even | 2 | 1 | 336.10.a.a | 1 | ||
21.c | even | 2 | 1 | 294.10.a.d | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
42.10.a.c | ✓ | 1 | 3.b | odd | 2 | 1 | |
126.10.a.h | 1 | 1.a | even | 1 | 1 | trivial | |
294.10.a.d | 1 | 21.c | even | 2 | 1 | ||
336.10.a.a | 1 | 12.b | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} - 2290 \)
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(126))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 16 \)
$3$
\( T \)
$5$
\( T - 2290 \)
$7$
\( T + 2401 \)
$11$
\( T + 64468 \)
$13$
\( T + 174402 \)
$17$
\( T + 441322 \)
$19$
\( T + 506332 \)
$23$
\( T + 1104880 \)
$29$
\( T + 6115454 \)
$31$
\( T - 2827296 \)
$37$
\( T - 9341222 \)
$41$
\( T - 12641454 \)
$43$
\( T - 30847772 \)
$47$
\( T - 4249824 \)
$53$
\( T + 87962982 \)
$59$
\( T - 5995348 \)
$61$
\( T + 672930 \)
$67$
\( T + 140689148 \)
$71$
\( T - 322386224 \)
$73$
\( T - 281507290 \)
$79$
\( T + 466481136 \)
$83$
\( T + 495155764 \)
$89$
\( T - 524640510 \)
$97$
\( T - 1666701490 \)
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