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
|
| \(2\) |
\(1\) |
| \(5\) |
\(1\) |
| \(23\) |
\(1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{2} - 6 T_{3} - 279 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(230))\).
| $p$ |
$F_p(T)$ |
| $2$ |
\( ( 4 + T )^{2} \) |
| $3$ |
\( -279 - 6 T + T^{2} \) |
| $5$ |
\( ( 25 + T )^{2} \) |
| $7$ |
\( -964 + 164 T + T^{2} \) |
| $11$ |
\( 43336 - 488 T + T^{2} \) |
| $13$ |
\( 106393 - 738 T + T^{2} \) |
| $17$ |
\( -30352 - 1112 T + T^{2} \) |
| $19$ |
\( 481464 + 1584 T + T^{2} \) |
| $23$ |
\( ( 529 + T )^{2} \) |
| $29$ |
\( -33247567 + 2158 T + T^{2} \) |
| $31$ |
\( -48408031 - 3418 T + T^{2} \) |
| $37$ |
\( 3464 + 152 T + T^{2} \) |
| $41$ |
\( 237235849 + 31482 T + T^{2} \) |
| $43$ |
\( -308196 - 468 T + T^{2} \) |
| $47$ |
\( -33009039 - 10062 T + T^{2} \) |
| $53$ |
\( -256334812 - 3380 T + T^{2} \) |
| $59$ |
\( -375613664 + 42512 T + T^{2} \) |
| $61$ |
\( 264688648 + 44472 T + T^{2} \) |
| $67$ |
\( 3527283128 + 119392 T + T^{2} \) |
| $71$ |
\( 277583257 + 36126 T + T^{2} \) |
| $73$ |
\( -556133983 + 39514 T + T^{2} \) |
| $79$ |
\( -4014464456 - 6768 T + T^{2} \) |
| $83$ |
\( 3075302432 - 124304 T + T^{2} \) |
| $89$ |
\( -440349764 + 4356 T + T^{2} \) |
| $97$ |
\( 4764185692 - 139980 T + T^{2} \) |
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