Newspace parameters
| Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 200.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(32.0767639626\) |
| Analytic rank: | \(1\) |
| Dimension: | \(1\) |
| Coefficient field: | \(\mathbb{Q}\) |
| Coefficient ring: | \(\mathbb{Z}\) |
| Coefficient ring index: | \( 1 \) |
| Twist minimal: | no (minimal twist has level 40) |
| 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 |
|
0 | 8.00000 | 0 | 0 | 0 | 108.000 | 0 | −179.000 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(2\) | \(1\) |
| \(5\) | \(1\) |
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 | 200.6.a.c | 1 | |
| 4.b | odd | 2 | 1 | 400.6.a.f | 1 | ||
| 5.b | even | 2 | 1 | 40.6.a.b | ✓ | 1 | |
| 5.c | odd | 4 | 2 | 200.6.c.c | 2 | ||
| 15.d | odd | 2 | 1 | 360.6.a.b | 1 | ||
| 20.d | odd | 2 | 1 | 80.6.a.f | 1 | ||
| 20.e | even | 4 | 2 | 400.6.c.h | 2 | ||
| 40.e | odd | 2 | 1 | 320.6.a.e | 1 | ||
| 40.f | even | 2 | 1 | 320.6.a.l | 1 | ||
| 60.h | even | 2 | 1 | 720.6.a.h | 1 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 40.6.a.b | ✓ | 1 | 5.b | even | 2 | 1 | |
| 80.6.a.f | 1 | 20.d | odd | 2 | 1 | ||
| 200.6.a.c | 1 | 1.a | even | 1 | 1 | trivial | |
| 200.6.c.c | 2 | 5.c | odd | 4 | 2 | ||
| 320.6.a.e | 1 | 40.e | odd | 2 | 1 | ||
| 320.6.a.l | 1 | 40.f | even | 2 | 1 | ||
| 360.6.a.b | 1 | 15.d | odd | 2 | 1 | ||
| 400.6.a.f | 1 | 4.b | odd | 2 | 1 | ||
| 400.6.c.h | 2 | 20.e | even | 4 | 2 | ||
| 720.6.a.h | 1 | 60.h | even | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} - 8 \)
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(200))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T - 8 \)
$5$
\( T \)
$7$
\( T - 108 \)
$11$
\( T + 604 \)
$13$
\( T - 306 \)
$17$
\( T + 930 \)
$19$
\( T + 1324 \)
$23$
\( T - 852 \)
$29$
\( T - 5902 \)
$31$
\( T + 3320 \)
$37$
\( T + 10774 \)
$41$
\( T + 17958 \)
$43$
\( T + 9264 \)
$47$
\( T - 9796 \)
$53$
\( T - 31434 \)
$59$
\( T - 33228 \)
$61$
\( T + 40210 \)
$67$
\( T + 58864 \)
$71$
\( T + 55312 \)
$73$
\( T + 27258 \)
$79$
\( T - 31456 \)
$83$
\( T + 24552 \)
$89$
\( T + 90854 \)
$97$
\( T + 154706 \)
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