Newspace parameters
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(19.9770907140\) |
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 |
|
−128.000 | 1350.00 | 16384.0 | −81060.0 | −172800. | 823543. | −2.09715e6 | −1.25264e7 | 1.03757e7 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(7\) | \(-1\) |
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 | 14.16.a.a | ✓ | 1 |
3.b | odd | 2 | 1 | 126.16.a.e | 1 | ||
4.b | odd | 2 | 1 | 112.16.a.a | 1 | ||
7.b | odd | 2 | 1 | 98.16.a.b | 1 | ||
7.c | even | 3 | 2 | 98.16.c.b | 2 | ||
7.d | odd | 6 | 2 | 98.16.c.c | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
14.16.a.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
98.16.a.b | 1 | 7.b | odd | 2 | 1 | ||
98.16.c.b | 2 | 7.c | even | 3 | 2 | ||
98.16.c.c | 2 | 7.d | odd | 6 | 2 | ||
112.16.a.a | 1 | 4.b | odd | 2 | 1 | ||
126.16.a.e | 1 | 3.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} - 1350 \)
acting on \(S_{16}^{\mathrm{new}}(\Gamma_0(14))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T + 128 \)
$3$
\( T - 1350 \)
$5$
\( T + 81060 \)
$7$
\( T - 823543 \)
$11$
\( T - 70121184 \)
$13$
\( T - 151469552 \)
$17$
\( T + 249756546 \)
$19$
\( T + 6476856550 \)
$23$
\( T + 21129196200 \)
$29$
\( T - 7794825354 \)
$31$
\( T + 95032053412 \)
$37$
\( T + 870082295470 \)
$41$
\( T - 1007666657262 \)
$43$
\( T - 155007585272 \)
$47$
\( T + 2551970135004 \)
$53$
\( T - 4047645687774 \)
$59$
\( T + 12599248786302 \)
$61$
\( T + 39925031318044 \)
$67$
\( T + 48423780261124 \)
$71$
\( T - 37693101366144 \)
$73$
\( T - 141416194574306 \)
$79$
\( T - 247020521013128 \)
$83$
\( T - 2788789610034 \)
$89$
\( T + 5839634731110 \)
$97$
\( T - 278027158065374 \)
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