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 \(x^{3} - 47 x - 106\):
| \(\beta_{0}\) | \(=\) | \( 1 \) |
| \(\beta_{1}\) | \(=\) | \( 3 \nu \) |
| \(\beta_{2}\) | \(=\) | \( \nu^{2} - 4 \nu - 31 \) |
| \(1\) | \(=\) | \(\beta_0\) |
| \(\nu\) | \(=\) | \(\beta_{1}\)\(/3\) |
| \(\nu^{2}\) | \(=\) | \((\)\(3 \beta_{2} + 4 \beta_{1} + 93\)\()/3\) |
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 \( T_{3}^{3} + 26 T_{3}^{2} + 9 T_{3} - 1620 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(230))\).
| $p$ |
$F_p(T)$ |
| $2$ |
\( ( 4 + T )^{3} \) |
| $3$ |
\( -1620 + 9 T + 26 T^{2} + T^{3} \) |
| $5$ |
\( ( -25 + T )^{3} \) |
| $7$ |
\( -779544 - 19316 T - T^{2} + T^{3} \) |
| $11$ |
\( 21004632 - 175884 T - 178 T^{2} + T^{3} \) |
| $13$ |
\( -16482042 - 217575 T + 236 T^{2} + T^{3} \) |
| $17$ |
\( 73501360 - 753600 T + 1683 T^{2} + T^{3} \) |
| $19$ |
\( -841047768 - 4848620 T + 194 T^{2} + T^{3} \) |
| $23$ |
\( ( -529 + T )^{3} \) |
| $29$ |
\( 809182077 - 570953 T - 6901 T^{2} + T^{3} \) |
| $31$ |
\( 30813892995 - 999581 T - 6119 T^{2} + T^{3} \) |
| $37$ |
\( 881126317804 - 143618332 T - 5185 T^{2} + T^{3} \) |
| $41$ |
\( 1050649591 + 152495 T - 6727 T^{2} + T^{3} \) |
| $43$ |
\( -1900451896320 - 8805224 T + 22988 T^{2} + T^{3} \) |
| $47$ |
\( -98633296700 + 31449305 T + 13730 T^{2} + T^{3} \) |
| $53$ |
\( 1549341371484 + 448711800 T + 38027 T^{2} + T^{3} \) |
| $59$ |
\( -22979507348832 - 564614168 T + 43715 T^{2} + T^{3} \) |
| $61$ |
\( -4638543486768 + 488088052 T + 51364 T^{2} + T^{3} \) |
| $67$ |
\( 4102954370460 + 828384804 T + 51891 T^{2} + T^{3} \) |
| $71$ |
\( -1521596424555 - 6946409 T + 25667 T^{2} + T^{3} \) |
| $73$ |
\( 4522640531874 + 2744414065 T + 108532 T^{2} + T^{3} \) |
| $79$ |
\( -11537777158848 - 1407646380 T + 224 T^{2} + T^{3} \) |
| $83$ |
\( -70485885180896 - 5764115016 T + 61071 T^{2} + T^{3} \) |
| $89$ |
\( -650267509666176 - 8889108840 T + 93372 T^{2} + T^{3} \) |
| $97$ |
\( -42022925072144 + 16517913168 T + 260238 T^{2} + T^{3} \) |
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