Newspace parameters
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(14.7643393337\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
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 | 2.00000 | 2.00000 | 4.00000 | 4.00000 | 0 | 0 | 1.00000 | 8.00000 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(43\) | \(-1\) |
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 | 1849.2.a.d | 1 | |
43.b | odd | 2 | 1 | 43.2.a.a | ✓ | 1 | |
129.d | even | 2 | 1 | 387.2.a.e | 1 | ||
172.d | even | 2 | 1 | 688.2.a.b | 1 | ||
215.d | odd | 2 | 1 | 1075.2.a.h | 1 | ||
215.g | even | 4 | 2 | 1075.2.b.b | 2 | ||
301.c | even | 2 | 1 | 2107.2.a.a | 1 | ||
344.e | even | 2 | 1 | 2752.2.a.b | 1 | ||
344.h | odd | 2 | 1 | 2752.2.a.f | 1 | ||
473.d | even | 2 | 1 | 5203.2.a.a | 1 | ||
516.h | odd | 2 | 1 | 6192.2.a.ba | 1 | ||
559.d | odd | 2 | 1 | 7267.2.a.a | 1 | ||
645.d | even | 2 | 1 | 9675.2.a.b | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
43.2.a.a | ✓ | 1 | 43.b | odd | 2 | 1 | |
387.2.a.e | 1 | 129.d | even | 2 | 1 | ||
688.2.a.b | 1 | 172.d | even | 2 | 1 | ||
1075.2.a.h | 1 | 215.d | odd | 2 | 1 | ||
1075.2.b.b | 2 | 215.g | even | 4 | 2 | ||
1849.2.a.d | 1 | 1.a | even | 1 | 1 | trivial | |
2107.2.a.a | 1 | 301.c | even | 2 | 1 | ||
2752.2.a.b | 1 | 344.e | even | 2 | 1 | ||
2752.2.a.f | 1 | 344.h | odd | 2 | 1 | ||
5203.2.a.a | 1 | 473.d | even | 2 | 1 | ||
6192.2.a.ba | 1 | 516.h | odd | 2 | 1 | ||
7267.2.a.a | 1 | 559.d | odd | 2 | 1 | ||
9675.2.a.b | 1 | 645.d | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} - 2 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1849))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 2 \)
$3$
\( T - 2 \)
$5$
\( T - 4 \)
$7$
\( T \)
$11$
\( T - 3 \)
$13$
\( T + 5 \)
$17$
\( T + 3 \)
$19$
\( T - 2 \)
$23$
\( T + 1 \)
$29$
\( T - 6 \)
$31$
\( T + 1 \)
$37$
\( T \)
$41$
\( T - 5 \)
$43$
\( T \)
$47$
\( T - 4 \)
$53$
\( T + 5 \)
$59$
\( T + 12 \)
$61$
\( T + 2 \)
$67$
\( T + 3 \)
$71$
\( T + 2 \)
$73$
\( T + 2 \)
$79$
\( T + 8 \)
$83$
\( T - 15 \)
$89$
\( T - 4 \)
$97$
\( T - 7 \)
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