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 \(x^{3} - x^{2} - 20 x + 26\):
| \(\beta_{0}\) | \(=\) | \( 1 \) |
| \(\beta_{1}\) | \(=\) | \( \nu \) |
| \(\beta_{2}\) | \(=\) | \( \nu^{2} + \nu - 14 \) |
| \(1\) | \(=\) | \(\beta_0\) |
| \(\nu\) | \(=\) | \(\beta_{1}\) |
| \(\nu^{2}\) | \(=\) | \(\beta_{2} - \beta_{1} + 14\) |
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
|
| \(3\) |
\(1\) |
| \(5\) |
\(1\) |
| \(11\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{3} + 4 T_{2}^{2} - 15 T_{2} - 44 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(165))\).
| $p$ |
$F_p(T)$ |
| $2$ |
\( -44 - 15 T + 4 T^{2} + T^{3} \) |
| $3$ |
\( ( 3 + T )^{3} \) |
| $5$ |
\( ( 5 + T )^{3} \) |
| $7$ |
\( -3744 - 428 T + 4 T^{2} + T^{3} \) |
| $11$ |
\( ( -11 + T )^{3} \) |
| $13$ |
\( -34144 - 3560 T + T^{3} \) |
| $17$ |
\( -235104 + 9680 T + 218 T^{2} + T^{3} \) |
| $19$ |
\( -30960 + 5376 T - 146 T^{2} + T^{3} \) |
| $23$ |
\( 1664 - 2672 T + 200 T^{2} + T^{3} \) |
| $29$ |
\( 3163056 - 54364 T - 68 T^{2} + T^{3} \) |
| $31$ |
\( -1812096 - 23232 T + 68 T^{2} + T^{3} \) |
| $37$ |
\( 618952 + 36460 T + 390 T^{2} + T^{3} \) |
| $41$ |
\( -4364208 - 26076 T + 196 T^{2} + T^{3} \) |
| $43$ |
\( -31273920 - 28668 T + 524 T^{2} + T^{3} \) |
| $47$ |
\( -20966976 - 135920 T + 60 T^{2} + T^{3} \) |
| $53$ |
\( 39574952 - 260852 T + 158 T^{2} + T^{3} \) |
| $59$ |
\( -84227264 + 64144 T + 1044 T^{2} + T^{3} \) |
| $61$ |
\( 22757384 - 60548 T - 642 T^{2} + T^{3} \) |
| $67$ |
\( 87537664 - 462208 T + 236 T^{2} + T^{3} \) |
| $71$ |
\( 6553600 - 129728 T + 544 T^{2} + T^{3} \) |
| $73$ |
\( -5609344 - 299576 T - 900 T^{2} + T^{3} \) |
| $79$ |
\( -14694992 + 562208 T + 1586 T^{2} + T^{3} \) |
| $83$ |
\( -924645384 - 307644 T + 1582 T^{2} + T^{3} \) |
| $89$ |
\( 293444632 + 1406940 T + 2122 T^{2} + T^{3} \) |
| $97$ |
\( -223543736 - 1291700 T - 618 T^{2} + T^{3} \) |
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