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 \(x^{3} - x^{2} - 23 x + 6\):
| \(\beta_{0}\) | \(=\) | \( 1 \) |
| \(\beta_{1}\) | \(=\) | \( \nu \) |
| \(\beta_{2}\) | \(=\) | \( \nu^{2} - \nu - 15 \) |
| \(1\) | \(=\) | \(\beta_0\) |
| \(\nu\) | \(=\) | \(\beta_{1}\) |
| \(\nu^{2}\) | \(=\) | \(\beta_{2} + \beta_{1} + 15\) |
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
|
| \(3\) |
\(-1\) |
| \(5\) |
\(1\) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(675))\):
| \( T_{2}^{3} + T_{2}^{2} - 23 T_{2} - 6 \) |
| \( T_{7}^{3} + 44 T_{7}^{2} + 552 T_{7} + 1800 \) |
| $p$ |
$F_p(T)$ |
| $2$ |
\( -6 - 23 T + T^{2} + T^{3} \) |
| $3$ |
\( T^{3} \) |
| $5$ |
\( T^{3} \) |
| $7$ |
\( 1800 + 552 T + 44 T^{2} + T^{3} \) |
| $11$ |
\( -83280 - 2612 T + 38 T^{2} + T^{3} \) |
| $13$ |
\( -100120 - 4576 T + 28 T^{2} + T^{3} \) |
| $17$ |
\( -553887 - 11477 T + 19 T^{2} + T^{3} \) |
| $19$ |
\( 525871 + 3587 T - 187 T^{2} + T^{3} \) |
| $23$ |
\( -2043981 - 23301 T + 81 T^{2} + T^{3} \) |
| $29$ |
\( -7892760 - 47768 T + 160 T^{2} + T^{3} \) |
| $31$ |
\( -246321 - 17973 T - 227 T^{2} + T^{3} \) |
| $37$ |
\( -13637080 - 99924 T + 78 T^{2} + T^{3} \) |
| $41$ |
\( 12116640 - 42812 T - 338 T^{2} + T^{3} \) |
| $43$ |
\( -18464560 - 159916 T + 22 T^{2} + T^{3} \) |
| $47$ |
\( -283200 + 54208 T + 472 T^{2} + T^{3} \) |
| $53$ |
\( 939789 + 61387 T - 521 T^{2} + T^{3} \) |
| $59$ |
\( -34131480 - 166448 T + 140 T^{2} + T^{3} \) |
| $61$ |
\( 1782607 - 2749 T - 595 T^{2} + T^{3} \) |
| $67$ |
\( -11295000 + 75948 T + 878 T^{2} + T^{3} \) |
| $71$ |
\( 280550880 - 583652 T - 602 T^{2} + T^{3} \) |
| $73$ |
\( -404091280 - 95908 T + 1294 T^{2} + T^{3} \) |
| $79$ |
\( -2010303 + 97059 T - 629 T^{2} + T^{3} \) |
| $83$ |
\( -346404411 - 365877 T + 1287 T^{2} + T^{3} \) |
| $89$ |
\( 74325600 + 1057572 T + 2154 T^{2} + T^{3} \) |
| $97$ |
\( 63595520 + 543936 T + 1392 T^{2} + T^{3} \) |
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