Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{2305}\).
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
|
| \(2\) |
\(-1\) |
| \(7\) |
\(1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{2} - 14 T_{3} - 57576 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(112))\).
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{2} \) |
| $3$ |
\( -57576 - 14 T + T^{2} \) |
| $5$ |
\( 846720 + 2730 T + T^{2} \) |
| $7$ |
\( ( 2401 + T )^{2} \) |
| $11$ |
\( -2036361600 + 44940 T + T^{2} \) |
| $13$ |
\( 2397429256 - 100282 T + T^{2} \) |
| $17$ |
\( 183575251116 + 870408 T + T^{2} \) |
| $19$ |
\( -352577596856 + 508774 T + T^{2} \) |
| $23$ |
\( -115915968000 + 79800 T + T^{2} \) |
| $29$ |
\( -31904129519604 - 2006328 T + T^{2} \) |
| $31$ |
\( -2367849772544 + 2188732 T + T^{2} \) |
| $37$ |
\( 60225113026444 + 20723576 T + T^{2} \) |
| $41$ |
\( -527816477266884 - 19016592 T + T^{2} \) |
| $43$ |
\( -271341247682336 + 4193716 T + T^{2} \) |
| $47$ |
\( 1296550084878144 - 74542524 T + T^{2} \) |
| $53$ |
\( -494746212296124 + 3239748 T + T^{2} \) |
| $59$ |
\( 1575046316366136 - 133642362 T + T^{2} \) |
| $61$ |
\( 11243934945943024 - 227801686 T + T^{2} \) |
| $67$ |
\( 21401918313456496 + 332930272 T + T^{2} \) |
| $71$ |
\( -85127259938918400 - 167985720 T + T^{2} \) |
| $73$ |
\( -83678371011966956 + 44684276 T + T^{2} \) |
| $79$ |
\( 6880003984764544 + 269642776 T + T^{2} \) |
| $83$ |
\( -76697718543013464 - 183105762 T + T^{2} \) |
| $89$ |
\( 50565747709419876 - 791657748 T + T^{2} \) |
| $97$ |
\( -451110491471642900 + 4169480 T + T^{2} \) |
|
show more
|
|
show less
|
