Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{17})\).
We also show the integral \(q\)-expansion of the trace form.
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
|
| \(3\) |
\(1\) |
| \(5\) |
\(1\) |
| \(7\) |
\(1\) |
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{2} + 7 T_{2} + 8 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(105))\).
Hecke Characteristic Polynomials
| $p$ |
$F_p(T)$ |
| $2$
| \( 1 + 7 T + 24 T^{2} + 56 T^{3} + 64 T^{4} \)
|
| $3$
| \( ( 1 + 3 T )^{2} \)
|
| $5$
| \( ( 1 + 5 T )^{2} \)
|
| $7$
| \( ( 1 + 7 T )^{2} \)
|
| $11$
| \( 1 + 26 T + 2406 T^{2} + 34606 T^{3} + 1771561 T^{4} \)
|
| $13$
| \( 1 - 14 T + 2386 T^{2} - 30758 T^{3} + 4826809 T^{4} \)
|
| $17$
| \( 1 - 16 T + 6558 T^{2} - 78608 T^{3} + 24137569 T^{4} \)
|
| $19$
| \( 1 - 174 T + 18414 T^{2} - 1193466 T^{3} + 47045881 T^{4} \)
|
| $23$
| \( 1 - 184 T + 19470 T^{2} - 2238728 T^{3} + 148035889 T^{4} \)
|
| $29$
| \( 1 + 32 T + 19046 T^{2} + 780448 T^{3} + 594823321 T^{4} \)
|
| $31$
| \( 1 - 330 T + 85430 T^{2} - 9831030 T^{3} + 887503681 T^{4} \)
|
| $37$
| \( 1 + 132 T + 103214 T^{2} + 6686196 T^{3} + 2565726409 T^{4} \)
|
| $41$
| \( 1 - 200 T + 64542 T^{2} - 13784200 T^{3} + 4750104241 T^{4} \)
|
| $43$
| \( 1 - 364 T + 172486 T^{2} - 28940548 T^{3} + 6321363049 T^{4} \)
|
| $47$
| \( 1 - 292 T + 179390 T^{2} - 30316316 T^{3} + 10779215329 T^{4} \)
|
| $53$
| \( 1 - 34 T + 103410 T^{2} - 5061818 T^{3} + 22164361129 T^{4} \)
|
| $59$
| \( 1 - 364 T + 438374 T^{2} - 74757956 T^{3} + 42180533641 T^{4} \)
|
| $61$
| \( 1 - 792 T + 340886 T^{2} - 179768952 T^{3} + 51520374361 T^{4} \)
|
| $67$
| \( 1 + 788 T + 753430 T^{2} + 237001244 T^{3} + 90458382169 T^{4} \)
|
| $71$
| \( 1 - 454 T + 304526 T^{2} - 162491594 T^{3} + 128100283921 T^{4} \)
|
| $73$
| \( 1 - 778 T + 794698 T^{2} - 302655226 T^{3} + 151334226289 T^{4} \)
|
| $79$
| \( 1 - 408 T + 994782 T^{2} - 201159912 T^{3} + 243087455521 T^{4} \)
|
| $83$
| \( 1 - 1136 T + 1169990 T^{2} - 649550032 T^{3} + 326940373369 T^{4} \)
|
| $89$
| \( 1 - 36 T - 842170 T^{2} - 25378884 T^{3} + 496981290961 T^{4} \)
|
| $97$
| \( 1 + 498 T + 1796754 T^{2} + 454511154 T^{3} + 832972004929 T^{4} \)
|
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