Newspace parameters
| Level: | \( N \) | = | \( 3 \) |
| Weight: | \( k \) | = | \( 20 \) |
| Character orbit: | \([\chi]\) | = | 3.a (trivial) |
Newform invariants
| Self dual: | Yes |
| Analytic conductor: | \(6.86450089669\) |
| Analytic rank: | \(0\) |
| Dimension: | \(2\) |
| Coefficient field: | \(\Q(\sqrt{87481}) \) |
| Coefficient ring: | \(\Z[a_1, a_2]\) |
| Coefficient ring index: | \( 2\cdot 3 \) |
| Fricke sign: | \(1\) |
| Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 3\sqrt{87481}\). 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 |
|
−536.316 | −19683.0 | −236654. | −683163. | 1.05563e7 | 1.13677e8 | 4.08105e8 | 3.87420e8 | 3.66391e8 | ||||||||||||||||||||||||
| 1.2 | 1238.32 | −19683.0 | 1.00914e6 | 6.69930e6 | −2.43738e7 | 214621. | 6.00397e8 | 3.87420e8 | 8.29585e9 | |||||||||||||||||||||||||
Inner twists
This newform does not admit any (nontrivial) inner twists.
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(3\) | \(1\) |
Hecke kernels
This newform can be constructed as the kernel of the linear operator \(T_{2}^{2} \) \(\mathstrut -\mathstrut 702 T_{2} \) \(\mathstrut -\mathstrut 664128 \) acting on \(S_{20}^{\mathrm{new}}(\Gamma_0(3))\).