Newspace parameters
| Level: | \( N \) | \(=\) | \( 45738 = 2 \cdot 3^{3} \cdot 7 \cdot 11^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 45738.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(365.219768765\) |
| Dimension: | \(8\) |
| Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
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| Defining polynomial: |
\( x^{8} - 3x^{7} - 15x^{6} + 42x^{5} + 57x^{4} - 159x^{3} + x^{2} + 120x - 45 \)
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| 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 |
|---|---|
| \(2\) | \( +1 \) |
| \(3\) | \( -1 \) |
| \(7\) | \( +1 \) |
| \(11\) | \( +1 \) |
Inner twists
Inner twists of this newform have not been computed.
Twists
Twists of this newform have not been computed.