Newspace parameters
Level: | \( N \) | = | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 65.a (trivial) |
Newform invariants
Self dual: | Yes |
Analytic conductor: | \(0.519027613138\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{3}) \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{3}\). 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 |
|
−1.73205 | 2.73205 | 1.00000 | −1.00000 | −4.73205 | 2.00000 | 1.73205 | 4.46410 | 1.73205 | ||||||||||||||||||||||||
1.2 | 1.73205 | −0.732051 | 1.00000 | −1.00000 | −1.26795 | 2.00000 | −1.73205 | −2.46410 | −1.73205 |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(5\) | \(1\) |
\(13\) | \(-1\) |
Hecke kernels
This newform can be constructed as the kernel of the linear operator \( T_{2}^{2} - 3 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(65))\).