Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2\) for the coefficient ring described below.
We also show the integral \(q\)-expansion of the trace form.
Basis of coefficient ring in terms of a root \(\nu\) of \(x^{3} - 6 x - 3\):
| \(\beta_{0}\) | \(=\) | \( 1 \) |
| \(\beta_{1}\) | \(=\) | \( \nu \) |
| \(\beta_{2}\) | \(=\) | \( \nu^{2} - \nu - 4 \) |
| \(1\) | \(=\) | \(\beta_0\) |
| \(\nu\) | \(=\) | \(\beta_{1}\) |
| \(\nu^{2}\) | \(=\) | \(\beta_{2} + \beta_{1} + 4\) |
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.
| \( p \) |
Sign
|
| \(2\) |
\(1\) |
| \(5\) |
\(1\) |
| \(23\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{3} - 6 T_{3} - 3 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(920))\).
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} \) |
| $3$ |
\( -3 - 6 T + T^{3} \) |
| $5$ |
\( ( 1 + T )^{3} \) |
| $7$ |
\( 2 - 3 T - 3 T^{2} + T^{3} \) |
| $11$ |
\( -12 - 15 T - 3 T^{2} + T^{3} \) |
| $13$ |
\( 29 - 18 T + T^{3} \) |
| $17$ |
\( 12 - 15 T + 3 T^{2} + T^{3} \) |
| $19$ |
\( -48 - 33 T - 3 T^{2} + T^{3} \) |
| $23$ |
\( ( -1 + T )^{3} \) |
| $29$ |
\( 12 - 6 T - 3 T^{2} + T^{3} \) |
| $31$ |
\( 249 - 42 T - 6 T^{2} + T^{3} \) |
| $37$ |
\( ( -4 + T )^{3} \) |
| $41$ |
\( -69 - 60 T + 6 T^{2} + T^{3} \) |
| $43$ |
\( 32 + 72 T - 18 T^{2} + T^{3} \) |
| $47$ |
\( -76 + 66 T - 15 T^{2} + T^{3} \) |
| $53$ |
\( 536 - 132 T - 6 T^{2} + T^{3} \) |
| $59$ |
\( 32 - 36 T - 6 T^{2} + T^{3} \) |
| $61$ |
\( -596 + 225 T - 27 T^{2} + T^{3} \) |
| $67$ |
\( 2944 - 240 T - 12 T^{2} + T^{3} \) |
| $71$ |
\( 203 - 60 T - 6 T^{2} + T^{3} \) |
| $73$ |
\( -588 - 42 T + 15 T^{2} + T^{3} \) |
| $79$ |
\( T^{3} \) |
| $83$ |
\( -64 - 60 T + 12 T^{2} + T^{3} \) |
| $89$ |
\( 608 + 264 T + 30 T^{2} + T^{3} \) |
| $97$ |
\( 138 - 69 T - 9 T^{2} + T^{3} \) |
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