Newspace parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(1.54510750849\) |
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 |
|
18.0000 | 81.0000 | −188.000 | −1530.00 | 1458.00 | 9128.00 | −12600.0 | 6561.00 | −27540.0 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
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 | 3.10.a.b | ✓ | 1 |
3.b | odd | 2 | 1 | 9.10.a.a | 1 | ||
4.b | odd | 2 | 1 | 48.10.a.a | 1 | ||
5.b | even | 2 | 1 | 75.10.a.b | 1 | ||
5.c | odd | 4 | 2 | 75.10.b.c | 2 | ||
7.b | odd | 2 | 1 | 147.10.a.c | 1 | ||
8.b | even | 2 | 1 | 192.10.a.g | 1 | ||
8.d | odd | 2 | 1 | 192.10.a.n | 1 | ||
9.c | even | 3 | 2 | 81.10.c.b | 2 | ||
9.d | odd | 6 | 2 | 81.10.c.d | 2 | ||
11.b | odd | 2 | 1 | 363.10.a.a | 1 | ||
12.b | even | 2 | 1 | 144.10.a.m | 1 | ||
15.d | odd | 2 | 1 | 225.10.a.e | 1 | ||
15.e | even | 4 | 2 | 225.10.b.c | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
3.10.a.b | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
9.10.a.a | 1 | 3.b | odd | 2 | 1 | ||
48.10.a.a | 1 | 4.b | odd | 2 | 1 | ||
75.10.a.b | 1 | 5.b | even | 2 | 1 | ||
75.10.b.c | 2 | 5.c | odd | 4 | 2 | ||
81.10.c.b | 2 | 9.c | even | 3 | 2 | ||
81.10.c.d | 2 | 9.d | odd | 6 | 2 | ||
144.10.a.m | 1 | 12.b | even | 2 | 1 | ||
147.10.a.c | 1 | 7.b | odd | 2 | 1 | ||
192.10.a.g | 1 | 8.b | even | 2 | 1 | ||
192.10.a.n | 1 | 8.d | odd | 2 | 1 | ||
225.10.a.e | 1 | 15.d | odd | 2 | 1 | ||
225.10.b.c | 2 | 15.e | even | 4 | 2 | ||
363.10.a.a | 1 | 11.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} - 18 \)
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(3))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 18 \)
$3$
\( T - 81 \)
$5$
\( T + 1530 \)
$7$
\( T - 9128 \)
$11$
\( T - 21132 \)
$13$
\( T - 31214 \)
$17$
\( T + 279342 \)
$19$
\( T - 144020 \)
$23$
\( T + 1763496 \)
$29$
\( T - 4692510 \)
$31$
\( T + 369088 \)
$37$
\( T - 9347078 \)
$41$
\( T + 7226838 \)
$43$
\( T + 23147476 \)
$47$
\( T - 22971888 \)
$53$
\( T - 78477174 \)
$59$
\( T + 20310660 \)
$61$
\( T + 179339938 \)
$67$
\( T - 274528388 \)
$71$
\( T + 36342648 \)
$73$
\( T + 247089526 \)
$79$
\( T - 191874800 \)
$83$
\( T + 276159276 \)
$89$
\( T + 678997350 \)
$97$
\( T + 567657502 \)
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