Newspace parameters
| Level: | \( N \) | \(=\) | \( 45570 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 31 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 45570.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(363.878282011\) |
| Dimension: | \(14\) |
| Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
|
|
|
| Defining polynomial: |
\( x^{14} - 2 x^{13} - 61 x^{12} + 72 x^{11} + 1181 x^{10} - 498 x^{9} - 8661 x^{8} + 832 x^{7} + 26435 x^{6} + \cdots - 47 \)
|
| Twist minimal: | not computed |
| Fricke sign: | \(+1\) |
| Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(2\) | \( +1 \) |
| \(3\) | \( -1 \) |
| \(5\) | \( -1 \) |
| \(7\) | \( +1 \) |
| \(31\) | \( +1 \) |
Inner twists
Inner twists of this newform have not been computed.
Twists
Twists of this newform have not been computed.