Newspace parameters
Level: | \( N \) | = | \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 6930.a (trivial) |
Newform invariants
Self dual: | Yes |
Analytic conductor: | \(55.3363286007\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
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 |
|
−1.00000 | 0 | 1.00000 | 1.00000 | 0 | 1.00000 | −1.00000 | 0 | −1.00000 |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(3\) | \(-1\) |
\(5\) | \(-1\) |
\(7\) | \(-1\) |
\(11\) | \(-1\) |
Hecke kernels
This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6930))\):
\( T_{13} + 4 \) |
\( T_{17} \) |
\( T_{19} + 4 \) |
\( T_{23} \) |
\( T_{29} - 6 \) |
\( T_{31} + 10 \) |