Newspace parameters
Level: | \( N \) | = | \( 4005 = 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 4005.a (trivial) |
Newform invariants
Self dual: | Yes |
Analytic conductor: | \(31.9800860095\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
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 \(\beta = \frac{1}{2}(1 + \sqrt{17})\). 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 |
|
−1.56155 | 0 | 0.438447 | −1.00000 | 0 | 0 | 2.43845 | 0 | 1.56155 | ||||||||||||||||||||||||
1.2 | 2.56155 | 0 | 4.56155 | −1.00000 | 0 | 0 | 6.56155 | 0 | −2.56155 |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(5\) | \(1\) |
\(89\) | \(1\) |
Hecke kernels
This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4005))\):
\( T_{2}^{2} - T_{2} - 4 \) |
\( T_{7} \) |
\( T_{11} + 4 \) |