Newspace parameters
| Level: | \( N \) | \(=\) | \( 30345 = 3 \cdot 5 \cdot 7 \cdot 17^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 30345.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(242.306044934\) |
| Dimension: | \(6\) |
| Coefficient field: | 6.6.933067472.1 |
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| Defining polynomial: |
\( x^{6} - 2x^{5} - 11x^{4} + 22x^{3} + 27x^{2} - 58x + 9 \)
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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 |
|---|---|
| \(3\) | \( +1 \) |
| \(5\) | \( +1 \) |
| \(7\) | \( -1 \) |
| \(17\) | \( +1 \) |
Inner twists
Inner twists of this newform have not been computed.
Twists
Twists of this newform have not been computed.