Newspace parameters
Level: | \( N \) | \(=\) | \( 66 = 2 \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 66.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(0.527012653340\) |
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 |
|
1.00000 | −1.00000 | 1.00000 | 2.00000 | −1.00000 | −4.00000 | 1.00000 | 1.00000 | 2.00000 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(3\) | \(1\) |
\(11\) | \(1\) |
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 | 66.2.a.b | ✓ | 1 |
3.b | odd | 2 | 1 | 198.2.a.a | 1 | ||
4.b | odd | 2 | 1 | 528.2.a.j | 1 | ||
5.b | even | 2 | 1 | 1650.2.a.k | 1 | ||
5.c | odd | 4 | 2 | 1650.2.c.e | 2 | ||
7.b | odd | 2 | 1 | 3234.2.a.t | 1 | ||
8.b | even | 2 | 1 | 2112.2.a.r | 1 | ||
8.d | odd | 2 | 1 | 2112.2.a.e | 1 | ||
9.c | even | 3 | 2 | 1782.2.e.e | 2 | ||
9.d | odd | 6 | 2 | 1782.2.e.v | 2 | ||
11.b | odd | 2 | 1 | 726.2.a.c | 1 | ||
11.c | even | 5 | 4 | 726.2.e.g | 4 | ||
11.d | odd | 10 | 4 | 726.2.e.o | 4 | ||
12.b | even | 2 | 1 | 1584.2.a.f | 1 | ||
15.d | odd | 2 | 1 | 4950.2.a.bu | 1 | ||
15.e | even | 4 | 2 | 4950.2.c.p | 2 | ||
21.c | even | 2 | 1 | 9702.2.a.x | 1 | ||
24.f | even | 2 | 1 | 6336.2.a.cj | 1 | ||
24.h | odd | 2 | 1 | 6336.2.a.bw | 1 | ||
33.d | even | 2 | 1 | 2178.2.a.g | 1 | ||
44.c | even | 2 | 1 | 5808.2.a.bc | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
66.2.a.b | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
198.2.a.a | 1 | 3.b | odd | 2 | 1 | ||
528.2.a.j | 1 | 4.b | odd | 2 | 1 | ||
726.2.a.c | 1 | 11.b | odd | 2 | 1 | ||
726.2.e.g | 4 | 11.c | even | 5 | 4 | ||
726.2.e.o | 4 | 11.d | odd | 10 | 4 | ||
1584.2.a.f | 1 | 12.b | even | 2 | 1 | ||
1650.2.a.k | 1 | 5.b | even | 2 | 1 | ||
1650.2.c.e | 2 | 5.c | odd | 4 | 2 | ||
1782.2.e.e | 2 | 9.c | even | 3 | 2 | ||
1782.2.e.v | 2 | 9.d | odd | 6 | 2 | ||
2112.2.a.e | 1 | 8.d | odd | 2 | 1 | ||
2112.2.a.r | 1 | 8.b | even | 2 | 1 | ||
2178.2.a.g | 1 | 33.d | even | 2 | 1 | ||
3234.2.a.t | 1 | 7.b | odd | 2 | 1 | ||
4950.2.a.bu | 1 | 15.d | odd | 2 | 1 | ||
4950.2.c.p | 2 | 15.e | even | 4 | 2 | ||
5808.2.a.bc | 1 | 44.c | even | 2 | 1 | ||
6336.2.a.bw | 1 | 24.h | odd | 2 | 1 | ||
6336.2.a.cj | 1 | 24.f | even | 2 | 1 | ||
9702.2.a.x | 1 | 21.c | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} - 2 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(66))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 1 \)
$3$
\( T + 1 \)
$5$
\( T - 2 \)
$7$
\( T + 4 \)
$11$
\( T + 1 \)
$13$
\( T + 6 \)
$17$
\( T - 2 \)
$19$
\( T - 4 \)
$23$
\( T - 4 \)
$29$
\( T - 6 \)
$31$
\( T \)
$37$
\( T - 6 \)
$41$
\( T + 6 \)
$43$
\( T - 4 \)
$47$
\( T + 12 \)
$53$
\( T - 2 \)
$59$
\( T - 12 \)
$61$
\( T + 14 \)
$67$
\( T - 4 \)
$71$
\( T + 12 \)
$73$
\( T + 6 \)
$79$
\( T + 4 \)
$83$
\( T - 4 \)
$89$
\( T - 10 \)
$97$
\( T + 14 \)
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