Newspace parameters
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(19.3015672113\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2) |
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 |
|
−64.0000 | 0 | 4096.00 | 57450.0 | 0 | 64232.0 | −262144. | 0 | −3.67680e6 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(3\) | \(-1\) |
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 | 18.14.a.c | 1 | |
3.b | odd | 2 | 1 | 2.14.a.b | ✓ | 1 | |
4.b | odd | 2 | 1 | 144.14.a.l | 1 | ||
12.b | even | 2 | 1 | 16.14.a.a | 1 | ||
15.d | odd | 2 | 1 | 50.14.a.a | 1 | ||
15.e | even | 4 | 2 | 50.14.b.d | 2 | ||
21.c | even | 2 | 1 | 98.14.a.c | 1 | ||
21.g | even | 6 | 2 | 98.14.c.d | 2 | ||
21.h | odd | 6 | 2 | 98.14.c.a | 2 | ||
24.f | even | 2 | 1 | 64.14.a.h | 1 | ||
24.h | odd | 2 | 1 | 64.14.a.b | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
2.14.a.b | ✓ | 1 | 3.b | odd | 2 | 1 | |
16.14.a.a | 1 | 12.b | even | 2 | 1 | ||
18.14.a.c | 1 | 1.a | even | 1 | 1 | trivial | |
50.14.a.a | 1 | 15.d | odd | 2 | 1 | ||
50.14.b.d | 2 | 15.e | even | 4 | 2 | ||
64.14.a.b | 1 | 24.h | odd | 2 | 1 | ||
64.14.a.h | 1 | 24.f | even | 2 | 1 | ||
98.14.a.c | 1 | 21.c | even | 2 | 1 | ||
98.14.c.a | 2 | 21.h | odd | 6 | 2 | ||
98.14.c.d | 2 | 21.g | even | 6 | 2 | ||
144.14.a.l | 1 | 4.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} - 57450 \)
acting on \(S_{14}^{\mathrm{new}}(\Gamma_0(18))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T + 64 \)
$3$
\( T \)
$5$
\( T - 57450 \)
$7$
\( T - 64232 \)
$11$
\( T + 2464572 \)
$13$
\( T - 8032766 \)
$17$
\( T + 71112402 \)
$19$
\( T - 136337060 \)
$23$
\( T - 1186563144 \)
$29$
\( T - 890583090 \)
$31$
\( T - 4595552672 \)
$37$
\( T + 19585053898 \)
$41$
\( T - 2724170358 \)
$43$
\( T - 51762321116 \)
$47$
\( T - 53572833168 \)
$53$
\( T + 82633440006 \)
$59$
\( T - 394266352980 \)
$61$
\( T - 671061772142 \)
$67$
\( T - 388156449812 \)
$71$
\( T - 388772243928 \)
$73$
\( T - 1540972938026 \)
$79$
\( T + 3306509559280 \)
$83$
\( T + 4931756967396 \)
$89$
\( T + 3502949738490 \)
$97$
\( T + 388932598558 \)
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