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 \(x^{3} - x^{2} - 9 x + 12\):
| \(\beta_{0}\) | \(=\) | \( 1 \) |
| \(\beta_{1}\) | \(=\) | \( \nu \) |
| \(\beta_{2}\) | \(=\) | \( \nu^{2} + \nu - 7 \) |
| \(1\) | \(=\) | \(\beta_0\) |
| \(\nu\) | \(=\) | \(\beta_{1}\) |
| \(\nu^{2}\) | \(=\) | \(\beta_{2} - \beta_{1} + 7\) |
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 \( T_{3}^{3} - T_{3}^{2} - 9 T_{3} + 12 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(230))\).
| $p$ |
$F_p(T)$ |
| $2$ |
\( ( -1 + T )^{3} \) |
| $3$ |
\( 12 - 9 T - T^{2} + T^{3} \) |
| $5$ |
\( ( 1 + T )^{3} \) |
| $7$ |
\( 64 - 21 T - 3 T^{2} + T^{3} \) |
| $11$ |
\( 144 - 39 T - 3 T^{2} + T^{3} \) |
| $13$ |
\( -18 - 15 T + T^{2} + T^{3} \) |
| $17$ |
\( -18 + 7 T + 7 T^{2} + T^{3} \) |
| $19$ |
\( 64 - 21 T - 3 T^{2} + T^{3} \) |
| $23$ |
\( ( 1 + T )^{3} \) |
| $29$ |
\( 24 - 32 T + 4 T^{2} + T^{3} \) |
| $31$ |
\( -8 - 7 T + 5 T^{2} + T^{3} \) |
| $37$ |
\( -32 - 40 T + 2 T^{2} + T^{3} \) |
| $41$ |
\( 186 - 59 T - T^{2} + T^{3} \) |
| $43$ |
\( ( -8 + T )^{3} \) |
| $47$ |
\( -288 + 4 T + 14 T^{2} + T^{3} \) |
| $53$ |
\( ( 6 + T )^{3} \) |
| $59$ |
\( 144 + 28 T - 14 T^{2} + T^{3} \) |
| $61$ |
\( 526 - 157 T - T^{2} + T^{3} \) |
| $67$ |
\( 384 - 144 T - 8 T^{2} + T^{3} \) |
| $71$ |
\( -24 + 31 T - 11 T^{2} + T^{3} \) |
| $73$ |
\( -248 - 40 T + 8 T^{2} + T^{3} \) |
| $79$ |
\( -1152 - 240 T + 4 T^{2} + T^{3} \) |
| $83$ |
\( 96 - 20 T - 8 T^{2} + T^{3} \) |
| $89$ |
\( 1152 - 48 T - 18 T^{2} + T^{3} \) |
| $97$ |
\( 166 + 279 T + 33 T^{2} + T^{3} \) |
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