Newspace parameters
Level: | \( N \) | \(=\) | \( 102 = 2 \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 102.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(6.01819482059\) |
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 |
|
2.00000 | −3.00000 | 4.00000 | 5.00000 | −6.00000 | 12.0000 | 8.00000 | 9.00000 | 10.0000 | |||||||||||||||||||||
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 | 102.4.a.d | ✓ | 1 |
3.b | odd | 2 | 1 | 306.4.a.a | 1 | ||
4.b | odd | 2 | 1 | 816.4.a.h | 1 | ||
12.b | even | 2 | 1 | 2448.4.a.g | 1 | ||
17.b | even | 2 | 1 | 1734.4.a.f | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
102.4.a.d | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
306.4.a.a | 1 | 3.b | odd | 2 | 1 | ||
816.4.a.h | 1 | 4.b | odd | 2 | 1 | ||
1734.4.a.f | 1 | 17.b | even | 2 | 1 | ||
2448.4.a.g | 1 | 12.b | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} - 5 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(102))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 2 \)
$3$
\( T + 3 \)
$5$
\( T - 5 \)
$7$
\( T - 12 \)
$11$
\( T - 37 \)
$13$
\( T - 19 \)
$17$
\( T - 17 \)
$19$
\( T - 37 \)
$23$
\( T + 3 \)
$29$
\( T + 86 \)
$31$
\( T + 142 \)
$37$
\( T + 296 \)
$41$
\( T + 121 \)
$43$
\( T - 3 \)
$47$
\( T - 402 \)
$53$
\( T - 174 \)
$59$
\( T - 270 \)
$61$
\( T + 520 \)
$67$
\( T + 780 \)
$71$
\( T - 84 \)
$73$
\( T + 302 \)
$79$
\( T - 178 \)
$83$
\( T - 698 \)
$89$
\( T - 1512 \)
$97$
\( T + 500 \)
show more
show less