Newspace parameters
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(146.442685796\) |
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 | −50652.0 | 0 | 2.37741e6 | 0 | −1.69175e7 | 0 | 1.40336e9 | 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 | 64.20.a.b | 1 | |
4.b | odd | 2 | 1 | 64.20.a.h | 1 | ||
8.b | even | 2 | 1 | 1.20.a.a | ✓ | 1 | |
8.d | odd | 2 | 1 | 16.20.a.a | 1 | ||
24.h | odd | 2 | 1 | 9.20.a.a | 1 | ||
40.f | even | 2 | 1 | 25.20.a.a | 1 | ||
40.i | odd | 4 | 2 | 25.20.b.a | 2 | ||
56.h | odd | 2 | 1 | 49.20.a.b | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1.20.a.a | ✓ | 1 | 8.b | even | 2 | 1 | |
9.20.a.a | 1 | 24.h | odd | 2 | 1 | ||
16.20.a.a | 1 | 8.d | odd | 2 | 1 | ||
25.20.a.a | 1 | 40.f | even | 2 | 1 | ||
25.20.b.a | 2 | 40.i | odd | 4 | 2 | ||
49.20.a.b | 1 | 56.h | odd | 2 | 1 | ||
64.20.a.b | 1 | 1.a | even | 1 | 1 | trivial | |
64.20.a.h | 1 | 4.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 50652 \)
acting on \(S_{20}^{\mathrm{new}}(\Gamma_0(64))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T + 50652 \)
$5$
\( T - 2377410 \)
$7$
\( T + 16917544 \)
$11$
\( T - 16212108 \)
$13$
\( T + 50421615062 \)
$17$
\( T - 225070099506 \)
$19$
\( T - 1710278572660 \)
$23$
\( T - 14036534788872 \)
$29$
\( T + 1137835269510 \)
$31$
\( T + 104626880141728 \)
$37$
\( T - 169392327370594 \)
$41$
\( T + 3309984750560838 \)
$43$
\( T + 1127913532193492 \)
$47$
\( T - 3498693987674256 \)
$53$
\( T + 29\!\cdots\!02 \)
$59$
\( T + 58\!\cdots\!20 \)
$61$
\( T + 23\!\cdots\!42 \)
$67$
\( T - 20\!\cdots\!44 \)
$71$
\( T + 17\!\cdots\!68 \)
$73$
\( T - 29\!\cdots\!22 \)
$79$
\( T + 92\!\cdots\!40 \)
$83$
\( T + 12\!\cdots\!32 \)
$89$
\( T - 43\!\cdots\!30 \)
$97$
\( T + 63\!\cdots\!94 \)
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