Base field \(\Q(\sqrt{85}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[19,19,-w + 2]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $54$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} + 27x^{8} + 253x^{6} + 968x^{4} + 1324x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}\frac{27}{2384}e^{9} + \frac{661}{2384}e^{7} + \frac{5387}{2384}e^{5} + \frac{4279}{596}e^{3} + \frac{4639}{596}e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
4 | $[4, 2, 2]$ | $\phantom{-}\frac{17}{596}e^{8} + \frac{361}{596}e^{6} + \frac{2255}{596}e^{4} + \frac{1851}{298}e^{2} - \frac{313}{149}$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{27}{2384}e^{9} + \frac{661}{2384}e^{7} + \frac{5387}{2384}e^{5} + \frac{4279}{596}e^{3} + \frac{5235}{596}e$ |
7 | $[7, 7, w]$ | $-\frac{39}{2384}e^{9} - \frac{1021}{2384}e^{7} - \frac{8907}{2384}e^{5} - \frac{3645}{298}e^{3} - \frac{7661}{596}e$ |
7 | $[7, 7, w + 6]$ | $-\frac{3}{596}e^{9} - \frac{45}{298}e^{7} - \frac{220}{149}e^{5} - \frac{3011}{596}e^{3} - \frac{915}{298}e$ |
17 | $[17, 17, w + 8]$ | $-\frac{3}{298}e^{9} - \frac{45}{149}e^{7} - \frac{440}{149}e^{5} - \frac{3011}{298}e^{3} - \frac{1064}{149}e$ |
19 | $[19, 19, w + 1]$ | $-\frac{1}{298}e^{8} - \frac{15}{149}e^{6} - \frac{97}{149}e^{4} + \frac{387}{298}e^{2} + \frac{1036}{149}$ |
19 | $[19, 19, w - 2]$ | $\phantom{-}1$ |
23 | $[23, 23, w + 9]$ | $-\frac{11}{2384}e^{9} - \frac{181}{2384}e^{7} + \frac{101}{2384}e^{5} + \frac{2517}{596}e^{3} + \frac{5549}{596}e$ |
23 | $[23, 23, w + 13]$ | $\phantom{-}\frac{27}{1192}e^{9} + \frac{661}{1192}e^{7} + \frac{5387}{1192}e^{5} + \frac{3981}{298}e^{3} + \frac{2255}{298}e$ |
37 | $[37, 37, w + 11]$ | $-\frac{13}{1192}e^{9} - \frac{241}{1192}e^{7} - \frac{883}{1192}e^{5} + \frac{1845}{596}e^{3} + \frac{2175}{149}e$ |
37 | $[37, 37, w + 25]$ | $-\frac{19}{1192}e^{9} - \frac{421}{1192}e^{7} - \frac{2643}{1192}e^{5} - \frac{583}{298}e^{3} + \frac{2541}{298}e$ |
59 | $[59, 59, 3w + 10]$ | $\phantom{-}\frac{17}{298}e^{8} + \frac{361}{298}e^{6} + \frac{2255}{298}e^{4} + \frac{1702}{149}e^{2} - \frac{1520}{149}$ |
59 | $[59, 59, 3w - 13]$ | $-\frac{21}{298}e^{8} - \frac{481}{298}e^{6} - \frac{3329}{298}e^{4} - \frac{3610}{149}e^{2} - \frac{2084}{149}$ |
73 | $[73, 73, w + 15]$ | $-\frac{93}{2384}e^{9} - \frac{2343}{2384}e^{7} - \frac{19681}{2384}e^{5} - \frac{3962}{149}e^{3} - \frac{15747}{596}e$ |
73 | $[73, 73, w + 57]$ | $\phantom{-}\frac{93}{2384}e^{9} + \frac{2343}{2384}e^{7} + \frac{19681}{2384}e^{5} + \frac{3962}{149}e^{3} + \frac{15747}{596}e$ |
89 | $[89, 89, -w - 10]$ | $\phantom{-}\frac{69}{596}e^{8} + \frac{1623}{596}e^{6} + \frac{12045}{596}e^{4} + \frac{7293}{149}e^{2} + \frac{3594}{149}$ |
89 | $[89, 89, w - 11]$ | $-\frac{19}{298}e^{8} - \frac{421}{298}e^{6} - \frac{2941}{298}e^{4} - \frac{3103}{149}e^{2} + \frac{910}{149}$ |
97 | $[97, 97, w + 22]$ | $\phantom{-}\frac{11}{1192}e^{9} + \frac{181}{1192}e^{7} - \frac{101}{1192}e^{5} - \frac{2517}{298}e^{3} - \frac{6145}{298}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19,19,-w + 2]$ | $-1$ |