Base field 3.3.1772.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x + 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[5, 5, -\frac{3}{2}w^{2} - \frac{1}{2}w + 15]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 4x^{9} - 7x^{8} - 41x^{7} - x^{6} + 125x^{5} + 59x^{4} - 136x^{3} - 81x^{2} + 45x + 27\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + 4]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w^{2} + 11]$ | $\phantom{-}\frac{1}{3}e^{9} + \frac{2}{3}e^{8} - 4e^{7} - 7e^{6} + 16e^{5} + \frac{67}{3}e^{4} - \frac{77}{3}e^{3} - \frac{77}{3}e^{2} + \frac{41}{3}e + 8$ |
| 3 | $[3, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 7]$ | $-\frac{4}{9}e^{9} - \frac{10}{9}e^{8} + \frac{43}{9}e^{7} + \frac{104}{9}e^{6} - \frac{143}{9}e^{5} - \frac{326}{9}e^{4} + \frac{172}{9}e^{3} + \frac{367}{9}e^{2} - \frac{17}{3}e - 13$ |
| 5 | $[5, 5, -\frac{3}{2}w^{2} - \frac{1}{2}w + 15]$ | $-1$ |
| 9 | $[9, 3, -\frac{1}{2}w^{2} + \frac{5}{2}w - 1]$ | $-\frac{2}{9}e^{9} - \frac{5}{9}e^{8} + \frac{17}{9}e^{7} + \frac{43}{9}e^{6} - \frac{31}{9}e^{5} - \frac{91}{9}e^{4} - \frac{4}{9}e^{3} + \frac{62}{9}e^{2} + \frac{5}{3}e - 4$ |
| 25 | $[25, 5, \frac{7}{2}w^{2} - \frac{31}{2}w + 9]$ | $-\frac{10}{9}e^{9} - \frac{28}{9}e^{8} + \frac{100}{9}e^{7} + \frac{290}{9}e^{6} - \frac{293}{9}e^{5} - \frac{893}{9}e^{4} + \frac{316}{9}e^{3} + \frac{943}{9}e^{2} - \frac{43}{3}e - 31$ |
| 29 | $[29, 29, -\frac{5}{2}w^{2} + \frac{1}{2}w + 29]$ | $\phantom{-}e^{9} + 3e^{8} - 10e^{7} - 31e^{6} + 29e^{5} + 95e^{4} - 27e^{3} - 101e^{2} + 4e + 30$ |
| 41 | $[41, 41, -w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{3}e^{9} + 2e^{8} - \frac{5}{3}e^{7} - \frac{64}{3}e^{6} - \frac{17}{3}e^{5} + 70e^{4} + 28e^{3} - 85e^{2} - \frac{62}{3}e + 25$ |
| 41 | $[41, 41, -\frac{1}{2}w^{2} - \frac{3}{2}w + 3]$ | $\phantom{-}\frac{1}{3}e^{9} + e^{8} - \frac{11}{3}e^{7} - \frac{37}{3}e^{6} + \frac{40}{3}e^{5} + 51e^{4} - 22e^{3} - 80e^{2} + \frac{37}{3}e + 31$ |
| 41 | $[41, 41, 2w + 7]$ | $-\frac{2}{3}e^{9} - \frac{5}{3}e^{8} + \frac{23}{3}e^{7} + \frac{49}{3}e^{6} - \frac{88}{3}e^{5} - \frac{133}{3}e^{4} + \frac{134}{3}e^{3} + \frac{113}{3}e^{2} - 19e - 6$ |
| 43 | $[43, 43, -\frac{7}{2}w^{2} - \frac{1}{2}w + 37]$ | $\phantom{-}\frac{8}{9}e^{9} + \frac{17}{9}e^{8} - \frac{89}{9}e^{7} - \frac{169}{9}e^{6} + \frac{319}{9}e^{5} + \frac{484}{9}e^{4} - \frac{458}{9}e^{3} - \frac{461}{9}e^{2} + \frac{74}{3}e + 11$ |
| 43 | $[43, 43, \frac{1}{2}w^{2} - \frac{9}{2}w + 3]$ | $\phantom{-}e^{9} + 3e^{8} - 10e^{7} - 31e^{6} + 29e^{5} + 94e^{4} - 28e^{3} - 95e^{2} + 8e + 23$ |
| 43 | $[43, 43, \frac{1}{2}w^{2} - \frac{1}{2}w + 1]$ | $\phantom{-}\frac{8}{9}e^{9} + \frac{17}{9}e^{8} - \frac{98}{9}e^{7} - \frac{178}{9}e^{6} + \frac{400}{9}e^{5} + \frac{556}{9}e^{4} - \frac{629}{9}e^{3} - \frac{623}{9}e^{2} + \frac{95}{3}e + 20$ |
| 47 | $[47, 47, -w^{2} + w + 15]$ | $-\frac{2}{9}e^{9} - \frac{11}{9}e^{8} - \frac{7}{9}e^{7} + \frac{94}{9}e^{6} + \frac{188}{9}e^{5} - \frac{184}{9}e^{4} - \frac{493}{9}e^{3} + \frac{5}{9}e^{2} + \frac{88}{3}e + 11$ |
| 53 | $[53, 53, -2w^{2} + 2w + 29]$ | $\phantom{-}\frac{5}{9}e^{9} + \frac{5}{9}e^{8} - \frac{59}{9}e^{7} - \frac{37}{9}e^{6} + \frac{223}{9}e^{5} + \frac{37}{9}e^{4} - \frac{302}{9}e^{3} + \frac{73}{9}e^{2} + \frac{20}{3}e - 5$ |
| 59 | $[59, 59, w^{2} - w - 13]$ | $-\frac{2}{3}e^{9} - \frac{7}{3}e^{8} + 6e^{7} + 25e^{6} - 13e^{5} - \frac{245}{3}e^{4} + \frac{10}{3}e^{3} + \frac{280}{3}e^{2} + \frac{11}{3}e - 34$ |
| 67 | $[67, 67, -\frac{1}{2}w^{2} + \frac{1}{2}w + 9]$ | $-\frac{19}{9}e^{9} - \frac{52}{9}e^{8} + \frac{193}{9}e^{7} + \frac{521}{9}e^{6} - \frac{587}{9}e^{5} - \frac{1508}{9}e^{4} + \frac{664}{9}e^{3} + \frac{1480}{9}e^{2} - \frac{86}{3}e - 50$ |
| 71 | $[71, 71, 2w - 3]$ | $\phantom{-}\frac{5}{9}e^{9} + \frac{14}{9}e^{8} - \frac{32}{9}e^{7} - \frac{109}{9}e^{6} - \frac{20}{9}e^{5} + \frac{136}{9}e^{4} + \frac{229}{9}e^{3} + \frac{172}{9}e^{2} - \frac{55}{3}e - 17$ |
| 73 | $[73, 73, \frac{3}{2}w^{2} - \frac{11}{2}w + 1]$ | $-\frac{1}{9}e^{9} - \frac{7}{9}e^{8} - \frac{14}{9}e^{7} + \frac{53}{9}e^{6} + \frac{205}{9}e^{5} - \frac{50}{9}e^{4} - \frac{569}{9}e^{3} - \frac{185}{9}e^{2} + \frac{103}{3}e + 22$ |
| 79 | $[79, 79, -\frac{3}{2}w^{2} + \frac{15}{2}w - 5]$ | $-\frac{1}{9}e^{9} - \frac{1}{9}e^{8} + \frac{19}{9}e^{7} + \frac{11}{9}e^{6} - \frac{140}{9}e^{5} - \frac{47}{9}e^{4} + \frac{433}{9}e^{3} + \frac{88}{9}e^{2} - \frac{130}{3}e - 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -\frac{3}{2}w^{2} - \frac{1}{2}w + 15]$ | $1$ |