Base field 6.6.1202933.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 6x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $29$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 8x^{7} + 16x^{6} - 16x^{5} - 73x^{4} - 33x^{3} + 57x^{2} + 50x + 10\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ | $\phantom{-}\frac{8}{17}e^{7} + \frac{53}{17}e^{6} + \frac{53}{17}e^{5} - \frac{220}{17}e^{4} - \frac{324}{17}e^{3} + \frac{207}{17}e^{2} + \frac{301}{17}e + \frac{18}{17}$ |
| 19 | $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ | $-\frac{11}{17}e^{7} - \frac{75}{17}e^{6} - \frac{92}{17}e^{5} + \frac{260}{17}e^{4} + \frac{488}{17}e^{3} - \frac{121}{17}e^{2} - \frac{416}{17}e - \frac{148}{17}$ |
| 23 | $[23, 23, -w^{2} + w + 2]$ | $-\frac{16}{17}e^{7} - \frac{123}{17}e^{6} - \frac{208}{17}e^{5} + \frac{372}{17}e^{4} + \frac{1073}{17}e^{3} + \frac{11}{17}e^{2} - \frac{1061}{17}e - \frac{410}{17}$ |
| 25 | $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ | $\phantom{-}\frac{16}{17}e^{7} + \frac{123}{17}e^{6} + \frac{225}{17}e^{5} - \frac{287}{17}e^{4} - \frac{1056}{17}e^{3} - \frac{283}{17}e^{2} + \frac{976}{17}e + \frac{478}{17}$ |
| 41 | $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ | $\phantom{-}1$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w]$ | $-\frac{26}{17}e^{7} - \frac{185}{17}e^{6} - \frac{253}{17}e^{5} + \frac{630}{17}e^{4} + \frac{1308}{17}e^{3} - \frac{303}{17}e^{2} - \frac{1110}{17}e - \frac{220}{17}$ |
| 53 | $[53, 53, w^{5} - 5w^{3} - 3w^{2} + w + 3]$ | $\phantom{-}\frac{28}{17}e^{7} + \frac{211}{17}e^{6} + \frac{347}{17}e^{5} - \frac{617}{17}e^{4} - \frac{1729}{17}e^{3} - \frac{100}{17}e^{2} + \frac{1504}{17}e + \frac{624}{17}$ |
| 59 | $[59, 59, 2w^{5} - 11w^{3} - 4w^{2} + 8w]$ | $-\frac{3}{17}e^{7} - \frac{39}{17}e^{6} - \frac{141}{17}e^{5} - \frac{11}{17}e^{4} + \frac{623}{17}e^{3} + \frac{375}{17}e^{2} - \frac{693}{17}e - \frac{266}{17}$ |
| 61 | $[61, 61, w^{2} - 2w - 2]$ | $\phantom{-}\frac{4}{17}e^{7} + \frac{52}{17}e^{6} + \frac{171}{17}e^{5} - \frac{76}{17}e^{4} - \frac{876}{17}e^{3} - \frac{279}{17}e^{2} + \frac{1026}{17}e + \frac{332}{17}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{35}{17}e^{7} + \frac{251}{17}e^{6} + \frac{353}{17}e^{5} - \frac{852}{17}e^{4} - \frac{1902}{17}e^{3} + \frac{249}{17}e^{2} + \frac{1846}{17}e + \frac{695}{17}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + w - 3]$ | $\phantom{-}\frac{14}{17}e^{7} + \frac{131}{17}e^{6} + \frac{335}{17}e^{5} - \frac{181}{17}e^{4} - \frac{1519}{17}e^{3} - \frac{662}{17}e^{2} + \frac{1466}{17}e + \frac{652}{17}$ |
| 67 | $[67, 67, -2w^{4} + w^{3} + 10w^{2} - 6]$ | $\phantom{-}2e^{7} + 15e^{6} + 24e^{5} - 46e^{4} - 120e^{3} + 6e^{2} + 105e + 32$ |
| 73 | $[73, 73, w^{5} - 5w^{3} - 2w^{2} + 2w - 2]$ | $-\frac{32}{17}e^{7} - \frac{229}{17}e^{6} - \frac{314}{17}e^{5} + \frac{795}{17}e^{4} + \frac{1636}{17}e^{3} - \frac{454}{17}e^{2} - \frac{1510}{17}e - \frac{344}{17}$ |
| 73 | $[73, 73, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 2]$ | $-\frac{21}{17}e^{7} - \frac{137}{17}e^{6} - \frac{137}{17}e^{5} + \frac{518}{17}e^{4} + \frac{723}{17}e^{3} - \frac{435}{17}e^{2} - \frac{584}{17}e - \frac{94}{17}$ |
| 79 | $[79, 79, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$ | $\phantom{-}\frac{35}{17}e^{7} + \frac{251}{17}e^{6} + \frac{370}{17}e^{5} - \frac{767}{17}e^{4} - \frac{1885}{17}e^{3} + \frac{11}{17}e^{2} + \frac{1761}{17}e + \frac{644}{17}$ |
| 83 | $[83, 83, 2w^{5} - 11w^{3} - 4w^{2} + 6w]$ | $-\frac{45}{17}e^{7} - \frac{347}{17}e^{6} - \frac{602}{17}e^{5} + \frac{1008}{17}e^{4} + \frac{3123}{17}e^{3} + \frac{270}{17}e^{2} - \frac{3102}{17}e - \frac{1202}{17}$ |
| 89 | $[89, 89, -2w^{5} + 11w^{3} + 4w^{2} - 7w - 2]$ | $\phantom{-}\frac{45}{17}e^{7} + \frac{330}{17}e^{6} + \frac{500}{17}e^{5} - \frac{1059}{17}e^{4} - \frac{2647}{17}e^{3} + \frac{104}{17}e^{2} + \frac{2541}{17}e + \frac{896}{17}$ |
| 97 | $[97, 97, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}2e^{7} + 14e^{6} + 18e^{5} - 49e^{4} - 92e^{3} + 32e^{2} + 82e + 6$ |
| 97 | $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ | $-\frac{26}{17}e^{7} - \frac{202}{17}e^{6} - \frac{355}{17}e^{5} + \frac{562}{17}e^{4} + \frac{1733}{17}e^{3} + \frac{173}{17}e^{2} - \frac{1518}{17}e - \frac{696}{17}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ | $-1$ |