Newspace parameters
| Level: | \( N \) | \(=\) | \( 10470 = 2 \cdot 3 \cdot 5 \cdot 349 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 10470.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(83.6033709163\) |
| Dimension: | \(14\) |
| Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
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| Defining polynomial: |
\( x^{14} - x^{13} - 47 x^{12} + 91 x^{11} + 563 x^{10} - 1349 x^{9} - 1832 x^{8} + 5026 x^{7} + 2158 x^{6} + \cdots + 2 \)
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| Twist minimal: | yes |
| 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 |
|---|---|
| \(2\) | \( +1 \) |
| \(3\) | \( +1 \) |
| \(5\) | \( -1 \) |
| \(349\) | \( +1 \) |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
Twists of this newform have not been computed.