Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{29}\).
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 \( T_{2}^{2} - 116 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(69))\).
| $p$ |
$F_p(T)$ |
| $2$ |
\( -116 + T^{2} \) |
| $3$ |
\( ( 9 + T )^{2} \) |
| $5$ |
\( 2180 - 94 T + T^{2} \) |
| $7$ |
\( -28 + 118 T + T^{2} \) |
| $11$ |
\( -312656 - 320 T + T^{2} \) |
| $13$ |
\( -138068 + 288 T + T^{2} \) |
| $17$ |
\( 814124 + 1810 T + T^{2} \) |
| $19$ |
\( -2671684 - 730 T + T^{2} \) |
| $23$ |
\( ( -529 + T )^{2} \) |
| $29$ |
\( 14790892 - 8208 T + T^{2} \) |
| $31$ |
\( -65688688 - 1772 T + T^{2} \) |
| $37$ |
\( 132310492 + 23112 T + T^{2} \) |
| $41$ |
\( -46982572 - 5516 T + T^{2} \) |
| $43$ |
\( -179637860 - 10322 T + T^{2} \) |
| $47$ |
\( 422732560 - 42952 T + T^{2} \) |
| $53$ |
\( -392901044 + 25350 T + T^{2} \) |
| $59$ |
\( 76641728 - 18344 T + T^{2} \) |
| $61$ |
\( -105150020 - 37224 T + T^{2} \) |
| $67$ |
\( -601513940 + 7482 T + T^{2} \) |
| $71$ |
\( 3896171200 - 126848 T + T^{2} \) |
| $73$ |
\( 4595673524 - 137660 T + T^{2} \) |
| $79$ |
\( 906450660 - 62286 T + T^{2} \) |
| $83$ |
\( -1861324304 - 83120 T + T^{2} \) |
| $89$ |
\( 1061277044 - 69770 T + T^{2} \) |
| $97$ |
\( 4172745500 + 170104 T + T^{2} \) |
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