Base field 4.4.13525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 12x^{2} + 8x + 29\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 6x^{5} - 7x^{4} + 88x^{3} - 80x^{2} - 192x + 224\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ | $-\frac{1}{8}e^{5} + \frac{1}{2}e^{4} + \frac{15}{8}e^{3} - \frac{29}{4}e^{2} - \frac{9}{2}e + 16$ |
| 9 | $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ | $-1$ |
| 9 | $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ | $-\frac{19}{104}e^{5} + \frac{27}{52}e^{4} + \frac{309}{104}e^{3} - \frac{185}{26}e^{2} - \frac{111}{13}e + \frac{178}{13}$ |
| 11 | $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ | $\phantom{-}\frac{1}{13}e^{5} - \frac{23}{52}e^{4} - \frac{25}{26}e^{3} + \frac{333}{52}e^{2} + \frac{5}{13}e - \frac{142}{13}$ |
| 11 | $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ | $-\frac{1}{8}e^{5} + \frac{1}{2}e^{4} + \frac{15}{8}e^{3} - \frac{29}{4}e^{2} - \frac{7}{2}e + 16$ |
| 16 | $[16, 2, 2]$ | $-\frac{5}{52}e^{5} + \frac{19}{52}e^{4} + \frac{69}{52}e^{3} - \frac{231}{52}e^{2} - \frac{29}{13}e + \frac{41}{13}$ |
| 29 | $[29, 29, -w]$ | $\phantom{-}\frac{31}{104}e^{5} - \frac{55}{52}e^{4} - \frac{433}{104}e^{3} + \frac{373}{26}e^{2} + \frac{73}{13}e - \frac{326}{13}$ |
| 29 | $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ | $-\frac{5}{26}e^{5} + \frac{19}{26}e^{4} + \frac{69}{26}e^{3} - \frac{257}{26}e^{2} - \frac{58}{13}e + \frac{264}{13}$ |
| 41 | $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ | $-\frac{2}{13}e^{5} + \frac{33}{52}e^{4} + \frac{25}{13}e^{3} - \frac{471}{52}e^{2} - \frac{59}{26}e + \frac{284}{13}$ |
| 41 | $[41, 41, -w^{2} + 10]$ | $\phantom{-}\frac{1}{52}e^{5} - \frac{9}{52}e^{4} + \frac{7}{52}e^{3} + \frac{145}{52}e^{2} - \frac{67}{13}e - \frac{42}{13}$ |
| 41 | $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ | $\phantom{-}\frac{9}{26}e^{5} - \frac{29}{26}e^{4} - \frac{145}{26}e^{3} + \frac{421}{26}e^{2} + \frac{185}{13}e - \frac{418}{13}$ |
| 41 | $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ | $-\frac{5}{13}e^{5} + \frac{19}{13}e^{4} + \frac{69}{13}e^{3} - \frac{257}{13}e^{2} - \frac{103}{13}e + \frac{502}{13}$ |
| 49 | $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ | $-\frac{5}{26}e^{5} + \frac{19}{26}e^{4} + \frac{69}{26}e^{3} - \frac{283}{26}e^{2} - \frac{19}{13}e + \frac{290}{13}$ |
| 49 | $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{1}{4}e^{4} - \frac{15}{8}e^{3} + \frac{7}{2}e^{2} + 3e - 10$ |
| 59 | $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{5}{4}e^{4} - \frac{13}{4}e^{3} + \frac{73}{4}e^{2} + 4e - 36$ |
| 59 | $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ | $\phantom{-}\frac{2}{13}e^{5} - \frac{33}{52}e^{4} - \frac{25}{13}e^{3} + \frac{419}{52}e^{2} + \frac{7}{26}e - \frac{128}{13}$ |
| 61 | $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ | $-\frac{5}{26}e^{5} + \frac{25}{52}e^{4} + \frac{95}{26}e^{3} - \frac{371}{52}e^{2} - \frac{389}{26}e + \frac{238}{13}$ |
| 61 | $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ | $-\frac{5}{26}e^{5} + \frac{51}{52}e^{4} + \frac{69}{26}e^{3} - \frac{761}{52}e^{2} - \frac{129}{26}e + \frac{420}{13}$ |
| 71 | $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ | $\phantom{-}\frac{17}{52}e^{5} - \frac{9}{13}e^{4} - \frac{323}{52}e^{3} + \frac{251}{26}e^{2} + \frac{317}{13}e - \frac{246}{13}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ | $1$ |