Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 2\sqrt{2}\).
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
|
| \(3\) |
\(1\) |
| \(23\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{2} + 2 T_{2} - 7 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(69))\).
| $p$ |
$F_p(T)$ |
| $2$ |
\( -7 + 2 T + T^{2} \) |
| $3$ |
\( ( 3 + T )^{2} \) |
| $5$ |
\( -112 - 8 T + T^{2} \) |
| $7$ |
\( 188 + 28 T + T^{2} \) |
| $11$ |
\( 904 + 72 T + T^{2} \) |
| $13$ |
\( 612 + 60 T + T^{2} \) |
| $17$ |
\( 2104 - 96 T + T^{2} \) |
| $19$ |
\( 868 + 148 T + T^{2} \) |
| $23$ |
\( ( -23 + T )^{2} \) |
| $29$ |
\( -24444 + 204 T + T^{2} \) |
| $31$ |
\( -16272 + 168 T + T^{2} \) |
| $37$ |
\( -11428 - 116 T + T^{2} \) |
| $41$ |
\( -5404 - 4 T + T^{2} \) |
| $43$ |
\( 41508 + 420 T + T^{2} \) |
| $47$ |
\( -61376 + 48 T + T^{2} \) |
| $53$ |
\( -544 - 32 T + T^{2} \) |
| $59$ |
\( -199312 + 40 T + T^{2} \) |
| $61$ |
\( 126716 + 764 T + T^{2} \) |
| $67$ |
\( 73508 + 988 T + T^{2} \) |
| $71$ |
\( -641824 + 224 T + T^{2} \) |
| $73$ |
\( 143012 - 820 T + T^{2} \) |
| $79$ |
\( 757148 - 1772 T + T^{2} \) |
| $83$ |
\( 191432 - 1480 T + T^{2} \) |
| $89$ |
\( -365624 - 744 T + T^{2} \) |
| $97$ |
\( -1646588 + 260 T + T^{2} \) |
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