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 \(x^{3} - 14 x - 4\):
| \(\beta_{0}\) | \(=\) | \( 1 \) |
| \(\beta_{1}\) | \(=\) | \( \nu \) |
| \(\beta_{2}\) | \(=\) | \((\)\( \nu^{2} - 10 \)\()/2\) |
| \(1\) | \(=\) | \(\beta_0\) |
| \(\nu\) | \(=\) | \(\beta_{1}\) |
| \(\nu^{2}\) | \(=\) | \(2 \beta_{2} + 10\) |
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
|
| \(17\) |
\(1\) |
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{3} - T_{2}^{2} - 24 T_{2} + 32 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(17))\).
| $p$ |
$F_p(T)$ |
| $2$
| \( 1 - T + 16 T^{3} - 64 T^{5} + 512 T^{6} \)
|
| $3$
| \( 1 - 4 T + 19 T^{2} - 12 T^{3} + 513 T^{4} - 2916 T^{5} + 19683 T^{6} \)
|
| $5$
| \( 1 + 8 T + 331 T^{2} + 2032 T^{3} + 41375 T^{4} + 125000 T^{5} + 1953125 T^{6} \)
|
| $7$
| \( 1 - 22 T + 891 T^{2} - 14300 T^{3} + 305613 T^{4} - 2588278 T^{5} + 40353607 T^{6} \)
|
| $11$
| \( 1 + 28 T + 2627 T^{2} + 69844 T^{3} + 3496537 T^{4} + 49603708 T^{5} + 2357947691 T^{6} \)
|
| $13$
| \( 1 - 30 T + 5119 T^{2} - 141212 T^{3} + 11246443 T^{4} - 144804270 T^{5} + 10604499373 T^{6} \)
|
| $17$
| \( ( 1 + 17 T )^{3} \)
|
| $19$
| \( 1 - 80 T + 15945 T^{2} - 757312 T^{3} + 109366755 T^{4} - 3763670480 T^{5} + 322687697779 T^{6} \)
|
| $23$
| \( 1 - 142 T + 20731 T^{2} - 1854884 T^{3} + 252234077 T^{4} - 21021096238 T^{5} + 1801152661463 T^{6} \)
|
| $29$
| \( 1 + 456 T + 127075 T^{2} + 23761392 T^{3} + 3099232175 T^{4} + 271239434376 T^{5} + 14507145975869 T^{6} \)
|
| $31$
| \( 1 - 230 T + 77787 T^{2} - 13785468 T^{3} + 2317352517 T^{4} - 204125846630 T^{5} + 26439622160671 T^{6} \)
|
| $37$
| \( 1 - 356 T + 133995 T^{2} - 29888184 T^{3} + 6787248735 T^{4} - 913398601604 T^{5} + 129961739795077 T^{6} \)
|
| $41$
| \( 1 + 294 T + 120199 T^{2} + 38886804 T^{3} + 8284235279 T^{4} + 1396530646854 T^{5} + 327381934393961 T^{6} \)
|
| $43$
| \( 1 - 556 T + 289617 T^{2} - 81141512 T^{3} + 23026578819 T^{4} - 3514677855244 T^{5} + 502592611936843 T^{6} \)
|
| $47$
| \( 1 - 640 T + 396797 T^{2} - 134564608 T^{3} + 41196654931 T^{4} - 6898697810560 T^{5} + 1119130473102767 T^{6} \)
|
| $53$
| \( 1 - 302 T + 293171 T^{2} - 71759636 T^{3} + 43646418967 T^{4} - 6693637060958 T^{5} + 3299763591802133 T^{6} \)
|
| $59$
| \( 1 - 636 T + 514369 T^{2} - 211823016 T^{3} + 105640590851 T^{4} - 26826819395676 T^{5} + 8662995818654939 T^{6} \)
|
| $61$
| \( 1 + 84 T + 556531 T^{2} + 31340024 T^{3} + 126321962911 T^{4} + 4327711446324 T^{5} + 11694146092834141 T^{6} \)
|
| $67$
| \( 1 - 1008 T + 967329 T^{2} - 607104160 T^{3} + 290936772027 T^{4} - 91182049226352 T^{5} + 27206534396294947 T^{6} \)
|
| $71$
| \( 1 + 402 T + 483859 T^{2} + 12894428 T^{3} + 173178458549 T^{4} + 51496314136242 T^{5} + 45848500718449031 T^{6} \)
|
| $73$
| \( 1 - 838 T + 1394903 T^{2} - 671950004 T^{3} + 542640980351 T^{4} - 126818081630182 T^{5} + 58871586708267913 T^{6} \)
|
| $79$
| \( 1 + 594 T + 357843 T^{2} - 156405492 T^{3} + 176430554877 T^{4} + 144393948579474 T^{5} + 119851595982618319 T^{6} \)
|
| $83$
| \( 1 + 2396 T + 3204249 T^{2} + 2882084008 T^{3} + 1832147922963 T^{4} + 783349134592124 T^{5} + 186940255267540403 T^{6} \)
|
| $89$
| \( 1 + 170 T + 1042603 T^{2} - 206881916 T^{3} + 735002794307 T^{4} + 84486819463370 T^{5} + 350356403707485209 T^{6} \)
|
| $97$
| \( 1 + 270 T + 2151919 T^{2} + 286220420 T^{3} + 1963998369487 T^{4} + 224902441330830 T^{5} + 760231058654565217 T^{6} \)
|
|
show more
|
|
show less
|
