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 \(\nu = \zeta_{18} + \zeta_{18}^{-1}\):
\(\beta_{0}\) | \(=\) | \( 1 \) |
\(\beta_{1}\) | \(=\) | \( \nu \) |
\(\beta_{2}\) | \(=\) | \( \nu^{2} - 2 \) |
\(1\) | \(=\) | \(\beta_0\) |
\(\nu\) | \(=\) | \(\beta_{1}\) |
\(\nu^{2}\) | \(=\) | \(\beta_{2} + 2\) |
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.
This newform does not admit any (nontrivial) inner twists.
\( p \) |
Sign
|
\(3\) |
\(-1\) |
\(5\) |
\(1\) |
\(89\) |
\(1\) |
This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4005))\):
\( T_{2}^{3} - 3 T_{2} - 1 \) |
\( T_{7}^{3} - 3 T_{7}^{2} + 3 \) |
\( T_{11}^{3} - 6 T_{11}^{2} + 8 \) |