Newspace parameters
| Level: | \( N \) | = | \( 5 \) |
| Weight: | \( k \) | = | \( 8 \) |
| Character orbit: | \([\chi]\) | = | 5.a (trivial) |
Newform invariants
| Self dual: | Yes |
| Analytic conductor: | \(1.56192512742\) |
| Analytic rank: | \(0\) |
| Dimension: | \(2\) |
| Coefficient field: | \(\Q(\sqrt{19}) \) |
| Coefficient ring: | \(\Z[a_1, a_2]\) |
| Coefficient ring index: | \( 2 \) |
| Fricke sign: | \(1\) |
| Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 2\sqrt{19}\). We also show the integral \(q\)-expansion of the trace form.
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 |
|
1.28220 | 79.7424 | −126.356 | −125.000 | 102.246 | −538.197 | −326.136 | 4171.85 | −160.275 | ||||||||||||||||||||||||
| 1.2 | 18.7178 | −59.7424 | 222.356 | −125.000 | −1118.25 | 438.197 | 1766.14 | 1382.15 | −2339.72 | |||||||||||||||||||||||||
Inner twists
This newform does not admit any (nontrivial) inner twists.
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(5\) | \(1\) |
Hecke kernels
This newform can be constructed as the kernel of the linear operator \(T_{2}^{2} \) \(\mathstrut -\mathstrut 20 T_{2} \) \(\mathstrut +\mathstrut 24 \) acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(5))\).