Base field 4.4.19225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 15x^{2} + 2x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11,11,w + 3]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 14x^{5} + 16x^{4} + 27x^{3} - 43x^{2} + 8x + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ | $-\frac{2}{25}e^{6} - \frac{11}{25}e^{5} + \frac{1}{5}e^{4} + \frac{83}{25}e^{3} + \frac{3}{5}e^{2} - \frac{169}{25}e - \frac{8}{25}$ |
| 9 | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ | $-\frac{13}{25}e^{6} - \frac{34}{25}e^{5} + \frac{24}{5}e^{4} + \frac{152}{25}e^{3} - \frac{48}{5}e^{2} - \frac{136}{25}e + \frac{48}{25}$ |
| 9 | $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ | $\phantom{-}\frac{4}{5}e^{6} + \frac{7}{5}e^{5} - 9e^{4} - \frac{16}{5}e^{3} + 19e^{2} - \frac{12}{5}e - \frac{14}{5}$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ | $-\frac{4}{25}e^{6} + \frac{3}{25}e^{5} + \frac{12}{5}e^{4} - \frac{109}{25}e^{3} - \frac{29}{5}e^{2} + \frac{287}{25}e + \frac{9}{25}$ |
| 11 | $[11, 11, -w - 3]$ | $\phantom{-}1$ |
| 25 | $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ | $\phantom{-}\frac{13}{25}e^{6} + \frac{34}{25}e^{5} - \frac{24}{5}e^{4} - \frac{152}{25}e^{3} + \frac{53}{5}e^{2} + \frac{186}{25}e - \frac{198}{25}$ |
| 29 | $[29, 29, w + 1]$ | $\phantom{-}\frac{4}{25}e^{6} + \frac{22}{25}e^{5} - \frac{2}{5}e^{4} - \frac{141}{25}e^{3} + \frac{4}{5}e^{2} + \frac{138}{25}e - \frac{34}{25}$ |
| 29 | $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ | $\phantom{-}\frac{2}{5}e^{6} + \frac{1}{5}e^{5} - 6e^{4} + \frac{12}{5}e^{3} + 16e^{2} - \frac{51}{5}e - \frac{22}{5}$ |
| 31 | $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ | $\phantom{-}\frac{3}{5}e^{6} - \frac{1}{5}e^{5} - 9e^{4} + \frac{53}{5}e^{3} + 18e^{2} - \frac{124}{5}e + \frac{7}{5}$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ | $-\frac{6}{25}e^{6} - \frac{8}{25}e^{5} + \frac{13}{5}e^{4} - \frac{26}{25}e^{3} - \frac{21}{5}e^{2} + \frac{168}{25}e - \frac{24}{25}$ |
| 31 | $[31, 31, -w + 3]$ | $\phantom{-}\frac{24}{25}e^{6} + \frac{7}{25}e^{5} - \frac{67}{5}e^{4} + \frac{279}{25}e^{3} + \frac{149}{5}e^{2} - \frac{672}{25}e - \frac{104}{25}$ |
| 31 | $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ | $-\frac{7}{5}e^{6} - \frac{6}{5}e^{5} + 19e^{4} - \frac{27}{5}e^{3} - 46e^{2} + \frac{101}{5}e + \frac{47}{5}$ |
| 59 | $[59, 59, 2w^{2} - w - 13]$ | $\phantom{-}\frac{7}{25}e^{6} - \frac{24}{25}e^{5} - \frac{31}{5}e^{4} + \frac{322}{25}e^{3} + \frac{72}{5}e^{2} - \frac{646}{25}e + \frac{28}{25}$ |
| 59 | $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ | $-\frac{28}{25}e^{6} - \frac{29}{25}e^{5} + \frac{69}{5}e^{4} - \frac{113}{25}e^{3} - \frac{138}{5}e^{2} + \frac{434}{25}e + \frac{63}{25}$ |
| 61 | $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ | $-\frac{22}{25}e^{6} - \frac{21}{25}e^{5} + \frac{56}{5}e^{4} - \frac{87}{25}e^{3} - \frac{112}{5}e^{2} + \frac{391}{25}e - \frac{88}{25}$ |
| 61 | $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ | $-\frac{14}{25}e^{6} - \frac{27}{25}e^{5} + \frac{32}{5}e^{4} + \frac{81}{25}e^{3} - \frac{89}{5}e^{2} + \frac{42}{25}e + \frac{194}{25}$ |
| 71 | $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ | $\phantom{-}\frac{43}{25}e^{6} + \frac{49}{25}e^{5} - \frac{104}{5}e^{4} + \frac{153}{25}e^{3} + \frac{223}{5}e^{2} - \frac{654}{25}e - \frac{178}{25}$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ | $\phantom{-}\frac{14}{25}e^{6} + \frac{27}{25}e^{5} - \frac{22}{5}e^{4} + \frac{44}{25}e^{3} + \frac{4}{5}e^{2} - \frac{417}{25}e + \frac{306}{25}$ |
| 79 | $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ | $-\frac{64}{25}e^{6} - \frac{52}{25}e^{5} + \frac{172}{5}e^{4} - \frac{294}{25}e^{3} - \frac{394}{5}e^{2} + \frac{1017}{25}e + \frac{294}{25}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,w + 3]$ | $-1$ |