Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{11209}\).
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 \( T_{3}^{2} - 70 T_{3} - 9984 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(112))\).
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{2} \) |
| $3$ |
\( -9984 - 70 T + T^{2} \) |
| $5$ |
\( -3442720 - 1554 T + T^{2} \) |
| $7$ |
\( ( -2401 + T )^{2} \) |
| $11$ |
\( 601778720 + 62388 T + T^{2} \) |
| $13$ |
\( 3683031768 - 122766 T + T^{2} \) |
| $17$ |
\( -98587989700 - 73584 T + T^{2} \) |
| $19$ |
\( 297234258352 + 1171198 T + T^{2} \) |
| $23$ |
\( 657801801728 + 2262384 T + T^{2} \) |
| $29$ |
\( -6012588512356 + 1923360 T + T^{2} \) |
| $31$ |
\( -21751509340512 + 2977884 T + T^{2} \) |
| $37$ |
\( -162679566869060 + 13418528 T + T^{2} \) |
| $41$ |
\( 328158355074444 + 36367800 T + T^{2} \) |
| $43$ |
\( 89571104447680 - 21964916 T + T^{2} \) |
| $47$ |
\( -315559687006944 - 1362732 T + T^{2} \) |
| $53$ |
\( -5447527588396764 + 17898612 T + T^{2} \) |
| $59$ |
\( 11530429683334400 + 224710542 T + T^{2} \) |
| $61$ |
\( -17538476020200720 + 85847118 T + T^{2} \) |
| $67$ |
\( -17116249644144560 + 179568872 T + T^{2} \) |
| $71$ |
\( 13373504138731520 + 231378168 T + T^{2} \) |
| $73$ |
\( 1937721548439220 - 88098332 T + T^{2} \) |
| $79$ |
\( -82536692396593536 - 184274184 T + T^{2} \) |
| $83$ |
\( -72649117838539792 + 624641094 T + T^{2} \) |
| $89$ |
\( 570866059346416452 + 1574777148 T + T^{2} \) |
| $97$ |
\( -72492038224976036 - 213665984 T + T^{2} \) |
|
show more
|
|
show less
|
