Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19, 19, w + 1]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 15x^{5} + 79x^{4} - 151x^{3} - 46x^{2} + 453x - 364\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ | $\phantom{-}\frac{9}{29}e^{5} - \frac{98}{29}e^{4} + \frac{321}{29}e^{3} - \frac{136}{29}e^{2} - 30e + \frac{858}{29}$ |
9 | $[9, 3, -w^{3} + 8w + 8]$ | $\phantom{-}e$ |
16 | $[16, 2, 2]$ | $-\frac{14}{29}e^{5} + \frac{175}{29}e^{4} - \frac{683}{29}e^{3} + \frac{537}{29}e^{2} + 60e - \frac{2369}{29}$ |
19 | $[19, 19, w + 1]$ | $-1$ |
19 | $[19, 19, -w^{2} + 6]$ | $-\frac{19}{29}e^{5} + \frac{223}{29}e^{4} - \frac{813}{29}e^{3} + \frac{561}{29}e^{2} + 70e - \frac{2691}{29}$ |
19 | $[19, 19, -w^{2} + 2w + 5]$ | $\phantom{-}5$ |
19 | $[19, 19, -w + 2]$ | $-\frac{11}{29}e^{5} + \frac{123}{29}e^{4} - \frac{402}{29}e^{3} + \frac{134}{29}e^{2} + 36e - \frac{923}{29}$ |
25 | $[25, 5, 2w^{2} - 2w - 13]$ | $\phantom{-}\frac{1}{29}e^{5} - \frac{27}{29}e^{4} + \frac{171}{29}e^{3} - \frac{260}{29}e^{2} - 12e + \frac{685}{29}$ |
29 | $[29, 29, -w^{2} + 9]$ | $-\frac{25}{29}e^{5} + \frac{298}{29}e^{4} - \frac{1085}{29}e^{3} + \frac{671}{29}e^{2} + 96e - \frac{3292}{29}$ |
29 | $[29, 29, -w^{2} + 2w + 6]$ | $\phantom{-}\frac{24}{29}e^{5} - \frac{300}{29}e^{4} + \frac{1175}{29}e^{3} - \frac{933}{29}e^{2} - 104e + \frac{4144}{29}$ |
29 | $[29, 29, w^{2} - 7]$ | $-\frac{2}{29}e^{5} + \frac{25}{29}e^{4} - \frac{81}{29}e^{3} - \frac{2}{29}e^{2} + 7e + \frac{22}{29}$ |
29 | $[29, 29, -w^{2} + 2w + 8]$ | $\phantom{-}\frac{20}{29}e^{5} - \frac{221}{29}e^{4} + \frac{723}{29}e^{3} - \frac{299}{29}e^{2} - 63e + \frac{1955}{29}$ |
31 | $[31, 31, -2w^{2} + w + 12]$ | $\phantom{-}\frac{9}{29}e^{5} - \frac{98}{29}e^{4} + \frac{350}{29}e^{3} - \frac{310}{29}e^{2} - 27e + \frac{1235}{29}$ |
31 | $[31, 31, 2w^{2} - 3w - 11]$ | $\phantom{-}\frac{11}{29}e^{5} - \frac{181}{29}e^{4} + \frac{895}{29}e^{3} - \frac{1033}{29}e^{2} - 78e + \frac{3678}{29}$ |
41 | $[41, 41, -w]$ | $-\frac{2}{29}e^{5} + \frac{54}{29}e^{4} - \frac{342}{29}e^{3} + \frac{491}{29}e^{2} + 33e - \frac{1631}{29}$ |
41 | $[41, 41, -w + 1]$ | $-\frac{20}{29}e^{5} + \frac{250}{29}e^{4} - \frac{955}{29}e^{3} + \frac{647}{29}e^{2} + 86e - \frac{2970}{29}$ |
49 | $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ | $\phantom{-}\frac{17}{29}e^{5} - \frac{169}{29}e^{4} + \frac{500}{29}e^{3} - \frac{186}{29}e^{2} - 46e + \frac{1698}{29}$ |
49 | $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ | $-\frac{27}{29}e^{5} + \frac{265}{29}e^{4} - \frac{673}{29}e^{3} - \frac{230}{29}e^{2} + 64e - \frac{834}{29}$ |
61 | $[61, 61, 2w^{2} - 3w - 14]$ | $\phantom{-}e^{4} - 8e^{3} + 13e^{2} + 19e - 42$ |
61 | $[61, 61, 2w^{2} - w - 15]$ | $-\frac{4}{29}e^{5} + \frac{50}{29}e^{4} - \frac{191}{29}e^{3} + \frac{112}{29}e^{2} + 18e - \frac{246}{29}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, w + 1]$ | $1$ |