Base field 4.4.5725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 11\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 8x^{5} - 11x^{4} - 200x^{3} - 204x^{2} + 1175x + 2060\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w + 1]$ | $-\frac{20}{1541}e^{5} - \frac{178}{1541}e^{4} + \frac{16}{67}e^{3} + \frac{4023}{1541}e^{2} - \frac{2624}{1541}e - \frac{20314}{1541}$ |
| 11 | $[11, 11, w]$ | $-\frac{341}{1541}e^{5} - \frac{1648}{1541}e^{4} + \frac{380}{67}e^{3} + \frac{39082}{1541}e^{2} - \frac{52136}{1541}e - \frac{217372}{1541}$ |
| 11 | $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ | $\phantom{-}\frac{136}{1541}e^{5} + \frac{594}{1541}e^{4} - \frac{149}{67}e^{3} - \frac{12871}{1541}e^{2} + \frac{19076}{1541}e + \frac{62318}{1541}$ |
| 11 | $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ | $\phantom{-}\frac{30}{1541}e^{5} + \frac{267}{1541}e^{4} - \frac{24}{67}e^{3} - \frac{6805}{1541}e^{2} + \frac{2395}{1541}e + \frac{38176}{1541}$ |
| 11 | $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ | $\phantom{-}\frac{176}{1541}e^{5} + \frac{950}{1541}e^{4} - \frac{181}{67}e^{3} - \frac{22458}{1541}e^{2} + \frac{22783}{1541}e + \frac{121438}{1541}$ |
| 16 | $[16, 2, 2]$ | $-\frac{146}{1541}e^{5} - \frac{683}{1541}e^{4} + \frac{157}{67}e^{3} + \frac{15653}{1541}e^{2} - \frac{20388}{1541}e - \frac{87885}{1541}$ |
| 25 | $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ | $-\frac{205}{1541}e^{5} - \frac{1054}{1541}e^{4} + \frac{231}{67}e^{3} + \frac{26211}{1541}e^{2} - \frac{31519}{1541}e - \frac{155054}{1541}$ |
| 29 | $[29, 29, -w - 3]$ | $\phantom{-}\frac{10}{1541}e^{5} + \frac{89}{1541}e^{4} - \frac{8}{67}e^{3} - \frac{2782}{1541}e^{2} - \frac{1770}{1541}e + \frac{17862}{1541}$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ | $\phantom{-}\frac{350}{1541}e^{5} + \frac{1574}{1541}e^{4} - \frac{414}{67}e^{3} - \frac{37271}{1541}e^{2} + \frac{61330}{1541}e + \frac{206018}{1541}$ |
| 31 | $[31, 31, w^{3} - 6w + 1]$ | $\phantom{-}\frac{155}{1541}e^{5} + \frac{609}{1541}e^{4} - \frac{191}{67}e^{3} - \frac{13842}{1541}e^{2} + \frac{28041}{1541}e + \frac{71908}{1541}$ |
| 31 | $[31, 31, w^{3} - 6w - 2]$ | $\phantom{-}\frac{370}{1541}e^{5} + \frac{1752}{1541}e^{4} - \frac{430}{67}e^{3} - \frac{42835}{1541}e^{2} + \frac{63954}{1541}e + \frac{244824}{1541}$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ | $\phantom{-}1$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ | $-\frac{291}{1541}e^{5} - \frac{1203}{1541}e^{4} + \frac{340}{67}e^{3} + \frac{26713}{1541}e^{2} - \frac{50199}{1541}e - \frac{140390}{1541}$ |
| 59 | $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ | $-\frac{409}{1541}e^{5} - \frac{1945}{1541}e^{4} + \frac{421}{67}e^{3} + \frac{43206}{1541}e^{2} - \frac{50887}{1541}e - \frac{225416}{1541}$ |
| 59 | $[59, 59, w^{3} + w^{2} - 6w - 4]$ | $\phantom{-}\frac{281}{1541}e^{5} + \frac{1114}{1541}e^{4} - \frac{332}{67}e^{3} - \frac{25472}{1541}e^{2} + \frac{47346}{1541}e + \frac{131774}{1541}$ |
| 79 | $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ | $\phantom{-}\frac{525}{1541}e^{5} + \frac{2361}{1541}e^{4} - \frac{621}{67}e^{3} - \frac{56677}{1541}e^{2} + \frac{90454}{1541}e + \frac{313650}{1541}$ |
| 79 | $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ | $-\frac{28}{1541}e^{5} + \frac{59}{1541}e^{4} + \frac{76}{67}e^{3} + \frac{701}{1541}e^{2} - \frac{19700}{1541}e - \frac{16728}{1541}$ |
| 89 | $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ | $-\frac{642}{1541}e^{5} - \frac{2940}{1541}e^{4} + \frac{728}{67}e^{3} + \frac{70118}{1541}e^{2} - \frac{102106}{1541}e - \frac{400280}{1541}$ |
| 89 | $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ | $-\frac{8}{67}e^{5} - \frac{31}{67}e^{4} + \frac{241}{67}e^{3} + \frac{765}{67}e^{2} - \frac{1599}{67}e - \frac{4320}{67}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ | $-1$ |