Newspace parameters
| Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
| Weight: | \( k \) | \(=\) | \( 26 \) |
| Character orbit: | \([\chi]\) | \(=\) | 16.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(63.3594847924\) |
| Analytic rank: | \(0\) |
| Dimension: | \(1\) |
| Coefficient field: | \(\mathbb{Q}\) |
| Coefficient ring: | \(\mathbb{Z}\) |
| Coefficient ring index: | \( 1 \) |
| Twist minimal: | no (minimal twist has level 1) |
| 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 | 195804. | 0 | −7.41990e8 | 0 | −3.90806e10 | 0 | −8.08949e11 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(2\) | \(-1\) |
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 | 16.26.a.b | 1 | |
| 4.b | odd | 2 | 1 | 1.26.a.a | ✓ | 1 | |
| 12.b | even | 2 | 1 | 9.26.a.a | 1 | ||
| 20.d | odd | 2 | 1 | 25.26.a.a | 1 | ||
| 20.e | even | 4 | 2 | 25.26.b.a | 2 | ||
| 28.d | even | 2 | 1 | 49.26.a.a | 1 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 1.26.a.a | ✓ | 1 | 4.b | odd | 2 | 1 | |
| 9.26.a.a | 1 | 12.b | even | 2 | 1 | ||
| 16.26.a.b | 1 | 1.a | even | 1 | 1 | trivial | |
| 25.26.a.a | 1 | 20.d | odd | 2 | 1 | ||
| 25.26.b.a | 2 | 20.e | even | 4 | 2 | ||
| 49.26.a.a | 1 | 28.d | even | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} - 195804 \)
acting on \(S_{26}^{\mathrm{new}}(\Gamma_0(16))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T - 195804 \)
$5$
\( T + 741989850 \)
$7$
\( T + 39080597192 \)
$11$
\( T + 8419515299052 \)
$13$
\( T + 81651045335314 \)
$17$
\( T + 2519900028948078 \)
$19$
\( T - 6082056370308940 \)
$23$
\( T - 94\!\cdots\!24 \)
$29$
\( T + 27\!\cdots\!10 \)
$31$
\( T + 42\!\cdots\!52 \)
$37$
\( T - 20\!\cdots\!82 \)
$41$
\( T + 18\!\cdots\!98 \)
$43$
\( T + 30\!\cdots\!56 \)
$47$
\( T - 92\!\cdots\!88 \)
$53$
\( T + 99\!\cdots\!54 \)
$59$
\( T + 13\!\cdots\!80 \)
$61$
\( T - 90\!\cdots\!02 \)
$67$
\( T - 26\!\cdots\!28 \)
$71$
\( T - 19\!\cdots\!48 \)
$73$
\( T - 42\!\cdots\!26 \)
$79$
\( T - 27\!\cdots\!60 \)
$83$
\( T - 93\!\cdots\!84 \)
$89$
\( T + 17\!\cdots\!30 \)
$97$
\( T - 28\!\cdots\!62 \)
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