Newspace parameters
Level: | \( N \) | = | \( 8 = 2^{3} \) |
Weight: | \( k \) | = | \( 21 \) |
Character orbit: | \([\chi]\) | = | 8.d (of order \(2\) and degree \(1\)) |
Newform invariants
Self dual: | Yes |
Analytic conductor: | \(20.2811012082\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
$q$-expansion
Character Values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3.1 |
|
1024.00 | 114226. | 1.04858e6 | 0 | 1.16967e8 | 0 | 1.07374e9 | 9.56079e9 | 0 |
Inner twists
Char. orbit | Parity | Mult. | Self Twist | Proved |
---|---|---|---|---|
1.a | Even | 1 | trivial | yes |
8.d | Odd | 1 | CM by \(\Q(\sqrt{-2}) \) | yes |
Hecke kernels
This newform can be constructed as the kernel of the linear operator \( T_{3} - 114226 \) acting on \(S_{21}^{\mathrm{new}}(8, [\chi])\).