Base field 6.6.1997632.1
Generator \(w\), with minimal polynomial \(x^{6} - 8x^{4} + 19x^{2} - 13\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[41,41,-w^{3} - w^{2} + 3w + 4]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 23x^{3} - 20x^{2} + 9x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, w^{4} - 5w^{2} - w + 4]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w]$ | $-\frac{13}{50}e^{4} + \frac{7}{50}e^{3} + \frac{301}{50}e^{2} + \frac{23}{25}e - \frac{118}{25}$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}\frac{7}{50}e^{4} + \frac{1}{25}e^{3} - \frac{82}{25}e^{2} - \frac{219}{50}e + \frac{2}{25}$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $\phantom{-}\frac{7}{50}e^{4} + \frac{1}{25}e^{3} - \frac{82}{25}e^{2} - \frac{169}{50}e + \frac{102}{25}$ |
| 27 | $[27, 3, w^{5} - 6w^{3} + w^{2} + 8w - 2]$ | $-\frac{11}{25}e^{4} + \frac{33}{50}e^{3} + \frac{469}{50}e^{2} - \frac{251}{50}e - \frac{192}{25}$ |
| 27 | $[27, 3, w^{5} - 6w^{3} - w^{2} + 8w + 2]$ | $\phantom{-}\frac{34}{25}e^{4} - \frac{26}{25}e^{3} - \frac{768}{25}e^{2} - \frac{103}{25}e + \frac{398}{25}$ |
| 29 | $[29, 29, w^{4} - 6w^{2} + w + 8]$ | $-\frac{53}{50}e^{4} + \frac{21}{25}e^{3} + \frac{603}{25}e^{2} + \frac{101}{50}e - \frac{308}{25}$ |
| 29 | $[29, 29, -w^{4} + 6w^{2} + w - 8]$ | $-\frac{93}{50}e^{4} + \frac{77}{50}e^{3} + \frac{2061}{50}e^{2} + \frac{78}{25}e - \frac{498}{25}$ |
| 41 | $[41, 41, w^{3} - w^{2} - 3w + 4]$ | $-\frac{3}{10}e^{4} + \frac{1}{5}e^{3} + \frac{33}{5}e^{2} + \frac{11}{10}e - \frac{38}{5}$ |
| 41 | $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ | $\phantom{-}\frac{69}{50}e^{4} - \frac{33}{25}e^{3} - \frac{769}{25}e^{2} + \frac{177}{50}e + \frac{434}{25}$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 3]$ | $\phantom{-}\frac{27}{25}e^{4} - \frac{28}{25}e^{3} - \frac{604}{25}e^{2} + \frac{41}{25}e + \frac{394}{25}$ |
| 41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 8w - 6]$ | $\phantom{-}1$ |
| 43 | $[43, 43, -w^{4} + 6w^{2} - w - 9]$ | $\phantom{-}\frac{17}{50}e^{4} - \frac{13}{50}e^{3} - \frac{359}{50}e^{2} - \frac{7}{25}e + \frac{12}{25}$ |
| 43 | $[43, 43, -w^{4} + 6w^{2} + w - 9]$ | $-\frac{53}{50}e^{4} + \frac{21}{25}e^{3} + \frac{603}{25}e^{2} + \frac{101}{50}e - \frac{408}{25}$ |
| 49 | $[49, 7, w^{4} - 5w^{2} + 7]$ | $\phantom{-}\frac{7}{10}e^{4} - \frac{4}{5}e^{3} - \frac{77}{5}e^{2} + \frac{51}{10}e + \frac{42}{5}$ |
| 97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 4]$ | $\phantom{-}\frac{7}{50}e^{4} - \frac{23}{50}e^{3} - \frac{139}{50}e^{2} + \frac{128}{25}e + \frac{102}{25}$ |
| 97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 3]$ | $-\frac{7}{10}e^{4} + \frac{3}{10}e^{3} + \frac{159}{10}e^{2} + \frac{32}{5}e - \frac{52}{5}$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}\frac{23}{10}e^{4} - \frac{17}{10}e^{3} - \frac{521}{10}e^{2} - \frac{33}{5}e + \frac{148}{5}$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $\phantom{-}\frac{11}{25}e^{4} - \frac{29}{25}e^{3} - \frac{222}{25}e^{2} + \frac{363}{25}e + \frac{142}{25}$ |
| 113 | $[113, 113, w^{5} - w^{4} - 6w^{3} + 6w^{2} + 7w - 9]$ | $\phantom{-}\frac{31}{25}e^{4} - \frac{34}{25}e^{3} - \frac{687}{25}e^{2} + \frac{173}{25}e + \frac{432}{25}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41,41,-w^{3} - w^{2} + 3w + 4]$ | $-1$ |