Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{177})\).
We also show the integral \(q\)-expansion of the trace form.
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
|
| \(2\) |
\(-1\) |
| \(19\) |
\(1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1216))\):
| \( T_{3}^{2} - T_{3} - 44 \) |
| \( T_{5}^{2} + 10 T_{5} - 152 \) |
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{2} \) |
| $3$ |
\( -44 - T + T^{2} \) |
| $5$ |
\( -152 + 10 T + T^{2} \) |
| $7$ |
\( 768 + 57 T + T^{2} \) |
| $11$ |
\( -152 - 10 T + T^{2} \) |
| $13$ |
\( -2126 + 13 T + T^{2} \) |
| $17$ |
\( -9306 + 51 T + T^{2} \) |
| $19$ |
\( ( 19 + T )^{2} \) |
| $23$ |
\( -1472 - 155 T + T^{2} \) |
| $29$ |
\( -35654 - 79 T + T^{2} \) |
| $31$ |
\( -11264 - 16 T + T^{2} \) |
| $37$ |
\( 24772 + 380 T + T^{2} \) |
| $41$ |
\( 154432 + 790 T + T^{2} \) |
| $43$ |
\( -80048 - 296 T + T^{2} \) |
| $47$ |
\( -60800 - 200 T + T^{2} \) |
| $53$ |
\( 35818 + 397 T + T^{2} \) |
| $59$ |
\( -212964 - 201 T + T^{2} \) |
| $61$ |
\( 29932 - 680 T + T^{2} \) |
| $67$ |
\( 138612 + 939 T + T^{2} \) |
| $71$ |
\( 19792 + 406 T + T^{2} \) |
| $73$ |
\( 3738 - 123 T + T^{2} \) |
| $79$ |
\( -146048 + 106 T + T^{2} \) |
| $83$ |
\( 1237176 - 2226 T + T^{2} \) |
| $89$ |
\( 184800 + 870 T + T^{2} \) |
| $97$ |
\( 613036 + 1864 T + T^{2} \) |
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