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 14) |
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 | −560.000 | 0 | −2401.00 | 4096.00 | 0 | −8960.00 | |||||||||||||||||||||
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.e | 1 | |
3.b | odd | 2 | 1 | 14.10.a.a | ✓ | 1 | |
12.b | even | 2 | 1 | 112.10.a.b | 1 | ||
15.d | odd | 2 | 1 | 350.10.a.c | 1 | ||
15.e | even | 4 | 2 | 350.10.c.b | 2 | ||
21.c | even | 2 | 1 | 98.10.a.a | 1 | ||
21.g | even | 6 | 2 | 98.10.c.e | 2 | ||
21.h | odd | 6 | 2 | 98.10.c.f | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
14.10.a.a | ✓ | 1 | 3.b | odd | 2 | 1 | |
98.10.a.a | 1 | 21.c | even | 2 | 1 | ||
98.10.c.e | 2 | 21.g | even | 6 | 2 | ||
98.10.c.f | 2 | 21.h | odd | 6 | 2 | ||
112.10.a.b | 1 | 12.b | even | 2 | 1 | ||
126.10.a.e | 1 | 1.a | even | 1 | 1 | trivial | |
350.10.a.c | 1 | 15.d | odd | 2 | 1 | ||
350.10.c.b | 2 | 15.e | even | 4 | 2 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} + 560 \)
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(126))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 16 \)
$3$
\( T \)
$5$
\( T + 560 \)
$7$
\( T + 2401 \)
$11$
\( T - 54152 \)
$13$
\( T + 113172 \)
$17$
\( T + 6262 \)
$19$
\( T - 257078 \)
$23$
\( T - 266000 \)
$29$
\( T + 1574714 \)
$31$
\( T + 4637484 \)
$37$
\( T + 11946238 \)
$41$
\( T + 21909126 \)
$43$
\( T - 27520592 \)
$47$
\( T + 52927836 \)
$53$
\( T + 16221222 \)
$59$
\( T - 140509618 \)
$61$
\( T + 202963560 \)
$67$
\( T - 153734572 \)
$71$
\( T + 279655936 \)
$73$
\( T + 404022830 \)
$79$
\( T + 130689816 \)
$83$
\( T + 420134014 \)
$89$
\( T - 469542390 \)
$97$
\( T + 872501690 \)
show more
show less