Base field 4.4.2525.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 5\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[41,41,-w^{3} + w^{2} + 2w + 2]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 24x^{3} - 2x^{2} + 123x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w]$ | $-\frac{4}{199}e^{4} + \frac{15}{199}e^{3} - \frac{10}{199}e^{2} - \frac{253}{199}e + \frac{606}{199}$ |
5 | $[5, 5, w^{3} - 2w^{2} - 2w + 3]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{2} + 4]$ | $-\frac{4}{199}e^{4} + \frac{15}{199}e^{3} - \frac{10}{199}e^{2} - \frac{54}{199}e + \frac{606}{199}$ |
11 | $[11, 11, w^{2} - 2w - 3]$ | $-\frac{18}{199}e^{4} - \frac{32}{199}e^{3} + \frac{353}{199}e^{2} + \frac{354}{199}e - \frac{656}{199}$ |
16 | $[16, 2, 2]$ | $-\frac{25}{199}e^{4} + \frac{44}{199}e^{3} + \frac{435}{199}e^{2} - \frac{636}{199}e - \frac{1287}{199}$ |
29 | $[29, 29, w^{3} - 4w - 1]$ | $\phantom{-}\frac{10}{199}e^{4} + \frac{62}{199}e^{3} - \frac{174}{199}e^{2} - \frac{860}{199}e + \frac{674}{199}$ |
29 | $[29, 29, w^{3} - 3w^{2} - w + 4]$ | $\phantom{-}\frac{10}{199}e^{4} + \frac{62}{199}e^{3} - \frac{174}{199}e^{2} - \frac{860}{199}e + \frac{674}{199}$ |
41 | $[41, 41, w^{3} - 2w^{2} - w + 4]$ | $\phantom{-}\frac{33}{199}e^{4} - \frac{74}{199}e^{3} - \frac{614}{199}e^{2} + \frac{1142}{199}e + \frac{1866}{199}$ |
41 | $[41, 41, -w^{3} + w^{2} + 2w + 2]$ | $-1$ |
59 | $[59, 59, -2w^{3} + 4w^{2} + 4w - 7]$ | $\phantom{-}\frac{46}{199}e^{4} - \frac{73}{199}e^{3} - \frac{880}{199}e^{2} + \frac{820}{199}e + \frac{2384}{199}$ |
59 | $[59, 59, -3w^{2} + 2w + 7]$ | $\phantom{-}\frac{42}{199}e^{4} - \frac{58}{199}e^{3} - \frac{890}{199}e^{2} + \frac{368}{199}e + \frac{2990}{199}$ |
61 | $[61, 61, -w^{3} + 4w^{2} - 6]$ | $\phantom{-}\frac{18}{199}e^{4} + \frac{32}{199}e^{3} - \frac{552}{199}e^{2} - \frac{354}{199}e + \frac{3044}{199}$ |
61 | $[61, 61, w^{3} + w^{2} - 5w - 3]$ | $-\frac{9}{199}e^{4} - \frac{16}{199}e^{3} + \frac{276}{199}e^{2} + \frac{376}{199}e - \frac{2318}{199}$ |
71 | $[71, 71, w^{3} + w^{2} - 4w - 6]$ | $\phantom{-}\frac{42}{199}e^{4} - \frac{58}{199}e^{3} - \frac{890}{199}e^{2} + \frac{766}{199}e + \frac{2990}{199}$ |
71 | $[71, 71, 3w^{2} - 2w - 8]$ | $-\frac{14}{199}e^{4} - \frac{47}{199}e^{3} + \frac{164}{199}e^{2} + \frac{607}{199}e - \frac{466}{199}$ |
71 | $[71, 71, 3w^{2} - 4w - 7]$ | $\phantom{-}\frac{8}{199}e^{4} - \frac{30}{199}e^{3} + \frac{20}{199}e^{2} + \frac{108}{199}e - \frac{1610}{199}$ |
71 | $[71, 71, w^{3} - 4w^{2} + w + 8]$ | $-\frac{8}{199}e^{4} + \frac{30}{199}e^{3} + \frac{378}{199}e^{2} - \frac{506}{199}e - \frac{1176}{199}$ |
79 | $[79, 79, -2w^{3} + 3w^{2} + 5w - 2]$ | $\phantom{-}\frac{9}{199}e^{4} + \frac{16}{199}e^{3} + \frac{122}{199}e^{2} + \frac{22}{199}e - \frac{2856}{199}$ |
79 | $[79, 79, 2w^{2} - 3w - 7]$ | $\phantom{-}\frac{36}{199}e^{4} + \frac{64}{199}e^{3} - \frac{706}{199}e^{2} - \frac{708}{199}e + \frac{2506}{199}$ |
79 | $[79, 79, 2w^{2} - w - 8]$ | $-\frac{10}{199}e^{4} - \frac{62}{199}e^{3} + \frac{174}{199}e^{2} + \frac{1059}{199}e + \frac{520}{199}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$41$ | $[41,41,-w^{3} + w^{2} + 2w + 2]$ | $1$ |