Newspace parameters
Level: | \( N \) | = | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 65.f (of order \(4\) and degree \(2\)) |
Newform invariants
Self dual: | No |
Analytic conductor: | \(0.519027613138\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-1}) \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
$q$-expansion
Coefficients of the \(q\)-expansion are expressed in terms of \(i = \sqrt{-1}\). We also show the integral \(q\)-expansion of the trace form.
Character Values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(i\) | \(i\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
18.1 |
|
− | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | −2.00000 | + | 1.00000i | 1.00000 | − | 1.00000i | −2.00000 | − | 3.00000i | − | 1.00000i | 1.00000 | + | 2.00000i | |||||||||||||
47.1 | 1.00000i | 1.00000 | − | 1.00000i | 1.00000 | −2.00000 | − | 1.00000i | 1.00000 | + | 1.00000i | −2.00000 | 3.00000i | 1.00000i | 1.00000 | − | 2.00000i |
Inner twists
Char. orbit | Parity | Mult. | Self Twist | Proved |
---|---|---|---|---|
1.a | Even | 1 | trivial | yes |
65.f | Even | 1 | yes |
Hecke kernels
This newform can be constructed as the kernel of the linear operator \( T_{2}^{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(65, [\chi])\).