Newspace parameters
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(2.40575729719\) |
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 |
|
7.00000 | 9.00000 | 17.0000 | −25.0000 | 63.0000 | 12.0000 | −105.000 | 81.0000 | −175.000 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(5\) | \(1\) |
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 | 15.6.a.b | ✓ | 1 |
3.b | odd | 2 | 1 | 45.6.a.a | 1 | ||
4.b | odd | 2 | 1 | 240.6.a.b | 1 | ||
5.b | even | 2 | 1 | 75.6.a.a | 1 | ||
5.c | odd | 4 | 2 | 75.6.b.a | 2 | ||
7.b | odd | 2 | 1 | 735.6.a.b | 1 | ||
8.b | even | 2 | 1 | 960.6.a.k | 1 | ||
8.d | odd | 2 | 1 | 960.6.a.x | 1 | ||
12.b | even | 2 | 1 | 720.6.a.q | 1 | ||
15.d | odd | 2 | 1 | 225.6.a.h | 1 | ||
15.e | even | 4 | 2 | 225.6.b.a | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
15.6.a.b | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
45.6.a.a | 1 | 3.b | odd | 2 | 1 | ||
75.6.a.a | 1 | 5.b | even | 2 | 1 | ||
75.6.b.a | 2 | 5.c | odd | 4 | 2 | ||
225.6.a.h | 1 | 15.d | odd | 2 | 1 | ||
225.6.b.a | 2 | 15.e | even | 4 | 2 | ||
240.6.a.b | 1 | 4.b | odd | 2 | 1 | ||
720.6.a.q | 1 | 12.b | even | 2 | 1 | ||
735.6.a.b | 1 | 7.b | odd | 2 | 1 | ||
960.6.a.k | 1 | 8.b | even | 2 | 1 | ||
960.6.a.x | 1 | 8.d | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} - 7 \)
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(15))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 7 \)
$3$
\( T - 9 \)
$5$
\( T + 25 \)
$7$
\( T - 12 \)
$11$
\( T - 112 \)
$13$
\( T + 974 \)
$17$
\( T - 2182 \)
$19$
\( T - 1420 \)
$23$
\( T - 3216 \)
$29$
\( T + 4150 \)
$31$
\( T + 5688 \)
$37$
\( T - 6482 \)
$41$
\( T - 5402 \)
$43$
\( T + 21764 \)
$47$
\( T + 368 \)
$53$
\( T - 12586 \)
$59$
\( T + 25520 \)
$61$
\( T - 11782 \)
$67$
\( T + 13188 \)
$71$
\( T + 35968 \)
$73$
\( T - 73186 \)
$79$
\( T + 52440 \)
$83$
\( T - 69036 \)
$89$
\( T + 33870 \)
$97$
\( T - 143042 \)
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