Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2\) for the coefficient ring described below.
We also show the integral \(q\)-expansion of the trace form.
Basis of coefficient ring in terms of a root \(\nu\) of \(x^{3} - 98 x - 232\):
| \(\beta_{0}\) | \(=\) | \( 1 \) |
| \(\beta_{1}\) | \(=\) | \( \nu \) |
| \(\beta_{2}\) | \(=\) | \((\)\( \nu^{2} - 4 \nu - 66 \)\()/2\) |
| \(1\) | \(=\) | \(\beta_0\) |
| \(\nu\) | \(=\) | \(\beta_{1}\) |
| \(\nu^{2}\) | \(=\) | \(2 \beta_{2} + 4 \beta_{1} + 66\) |
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
|
| \(5\) |
\(-1\) |
| \(7\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(245))\):
| \( T_{2}^{3} + 6 T_{2}^{2} - 86 T_{2} - 420 \) |
| \( T_{3}^{3} + 26 T_{3}^{2} - 271 T_{3} - 6056 \) |
| $p$ |
$F_p(T)$ |
| $2$ |
\( -420 - 86 T + 6 T^{2} + T^{3} \) |
| $3$ |
\( -6056 - 271 T + 26 T^{2} + T^{3} \) |
| $5$ |
\( ( -25 + T )^{3} \) |
| $7$ |
\( T^{3} \) |
| $11$ |
\( -3144468 - 15583 T + 194 T^{2} + T^{3} \) |
| $13$ |
\( 171071930 + 1087501 T + 1892 T^{2} + T^{3} \) |
| $17$ |
\( -132716862 - 896603 T - 184 T^{2} + T^{3} \) |
| $19$ |
\( 140259040 - 2369180 T + 1212 T^{2} + T^{3} \) |
| $23$ |
\( 125424384 - 1476572 T - 3188 T^{2} + T^{3} \) |
| $29$ |
\( 51669601050 + 42201805 T + 11332 T^{2} + T^{3} \) |
| $31$ |
\( -8818293376 + 19282768 T + 9200 T^{2} + T^{3} \) |
| $37$ |
\( 1043894647208 - 190556324 T - 6042 T^{2} + T^{3} \) |
| $41$ |
\( -4748673370848 - 404569184 T + 10442 T^{2} + T^{3} \) |
| $43$ |
\( 4763987701360 - 99225644 T - 28112 T^{2} + T^{3} \) |
| $47$ |
\( 1072310433384 - 337915327 T + 2330 T^{2} + T^{3} \) |
| $53$ |
\( 515502653472 - 368369248 T - 7190 T^{2} + T^{3} \) |
| $59$ |
\( -7000620748800 - 362727680 T + 23760 T^{2} + T^{3} \) |
| $61$ |
\( 1590789613952 - 485040544 T + 8722 T^{2} + T^{3} \) |
| $67$ |
\( 26595134017984 + 2939620080 T + 97572 T^{2} + T^{3} \) |
| $71$ |
\( -77522711777280 - 1397406976 T + 52816 T^{2} + T^{3} \) |
| $73$ |
\( -11550435576632 - 3859440948 T + 34870 T^{2} + T^{3} \) |
| $79$ |
\( -40598762145400 - 279253695 T + 71546 T^{2} + T^{3} \) |
| $83$ |
\( 529374252288 - 2697140848 T - 20920 T^{2} + T^{3} \) |
| $89$ |
\( 31660963259040 + 8081767840 T - 192622 T^{2} + T^{3} \) |
| $97$ |
\( -117394067785166 - 7473101907 T + 116320 T^{2} + T^{3} \) |
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