Newspace parameters
Level: | \( N \) | \(=\) | \( 102 = 2 \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 102.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(0.814474100617\) |
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 | 0 | −1.00000 | 2.00000 | −1.00000 | 1.00000 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(3\) | \(-1\) |
\(17\) | \(1\) |
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 | 102.2.a.b | ✓ | 1 |
3.b | odd | 2 | 1 | 306.2.a.c | 1 | ||
4.b | odd | 2 | 1 | 816.2.a.d | 1 | ||
5.b | even | 2 | 1 | 2550.2.a.u | 1 | ||
5.c | odd | 4 | 2 | 2550.2.d.g | 2 | ||
7.b | odd | 2 | 1 | 4998.2.a.d | 1 | ||
8.b | even | 2 | 1 | 3264.2.a.i | 1 | ||
8.d | odd | 2 | 1 | 3264.2.a.w | 1 | ||
12.b | even | 2 | 1 | 2448.2.a.i | 1 | ||
15.d | odd | 2 | 1 | 7650.2.a.j | 1 | ||
17.b | even | 2 | 1 | 1734.2.a.b | 1 | ||
17.c | even | 4 | 2 | 1734.2.b.f | 2 | ||
17.d | even | 8 | 4 | 1734.2.f.b | 4 | ||
24.f | even | 2 | 1 | 9792.2.a.ba | 1 | ||
24.h | odd | 2 | 1 | 9792.2.a.bg | 1 | ||
51.c | odd | 2 | 1 | 5202.2.a.j | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
102.2.a.b | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
306.2.a.c | 1 | 3.b | odd | 2 | 1 | ||
816.2.a.d | 1 | 4.b | odd | 2 | 1 | ||
1734.2.a.b | 1 | 17.b | even | 2 | 1 | ||
1734.2.b.f | 2 | 17.c | even | 4 | 2 | ||
1734.2.f.b | 4 | 17.d | even | 8 | 4 | ||
2448.2.a.i | 1 | 12.b | even | 2 | 1 | ||
2550.2.a.u | 1 | 5.b | even | 2 | 1 | ||
2550.2.d.g | 2 | 5.c | odd | 4 | 2 | ||
3264.2.a.i | 1 | 8.b | even | 2 | 1 | ||
3264.2.a.w | 1 | 8.d | odd | 2 | 1 | ||
4998.2.a.d | 1 | 7.b | odd | 2 | 1 | ||
5202.2.a.j | 1 | 51.c | odd | 2 | 1 | ||
7650.2.a.j | 1 | 15.d | odd | 2 | 1 | ||
9792.2.a.ba | 1 | 24.f | even | 2 | 1 | ||
9792.2.a.bg | 1 | 24.h | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(102))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T + 1 \)
$3$
\( T - 1 \)
$5$
\( T \)
$7$
\( T - 2 \)
$11$
\( T \)
$13$
\( T - 2 \)
$17$
\( T + 1 \)
$19$
\( T + 4 \)
$23$
\( T + 6 \)
$29$
\( T \)
$31$
\( T + 10 \)
$37$
\( T - 8 \)
$41$
\( T - 6 \)
$43$
\( T + 4 \)
$47$
\( T - 12 \)
$53$
\( T - 6 \)
$59$
\( T + 12 \)
$61$
\( T - 8 \)
$67$
\( T + 4 \)
$71$
\( T - 6 \)
$73$
\( T - 2 \)
$79$
\( T + 10 \)
$83$
\( T - 12 \)
$89$
\( T + 18 \)
$97$
\( T - 14 \)
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