Base field 6.6.722000.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 7x^{3} + 4x^{2} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[49, 7, -3w^{5} + 2w^{4} + 19w^{3} - 15w^{2} - 19w + 9]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 6x^{7} - 5x^{6} + 71x^{5} - 16x^{4} - 264x^{3} + 55x^{2} + 283x + 25\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{5} + 6w^{3} - w^{2} - 6w]$ | $\phantom{-}e$ |
19 | $[19, 19, 3w^{5} - 2w^{4} - 19w^{3} + 14w^{2} + 18w - 9]$ | $\phantom{-}e^{2} - 2e - 5$ |
29 | $[29, 29, -w^{2} - w + 2]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{3}{2}e^{6} - 7e^{5} + \frac{31}{2}e^{4} + \frac{65}{2}e^{3} - \frac{65}{2}e^{2} - 36e + \frac{5}{2}$ |
29 | $[29, 29, 2w^{5} - w^{4} - 13w^{3} + 7w^{2} + 14w - 3]$ | $-\frac{3}{2}e^{7} + \frac{9}{2}e^{6} + 20e^{5} - \frac{85}{2}e^{4} - \frac{189}{2}e^{3} + \frac{153}{2}e^{2} + 122e + \frac{15}{2}$ |
29 | $[29, 29, -2w^{5} + w^{4} + 13w^{3} - 8w^{2} - 15w + 6]$ | $\phantom{-}e^{7} - 3e^{6} - \frac{27}{2}e^{5} + \frac{57}{2}e^{4} + \frac{131}{2}e^{3} - 53e^{2} - 89e - \frac{5}{2}$ |
49 | $[49, 7, -3w^{5} + 2w^{4} + 19w^{3} - 15w^{2} - 19w + 9]$ | $-1$ |
49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 6w^{2} + 9w - 4]$ | $\phantom{-}3e^{7} - \frac{17}{2}e^{6} - 42e^{5} + 80e^{4} + \frac{415}{2}e^{3} - 136e^{2} - \frac{557}{2}e - \frac{55}{2}$ |
49 | $[49, 7, w^{2} - 3]$ | $-e^{7} + 3e^{6} + 13e^{5} - 27e^{4} - 62e^{3} + 43e^{2} + 86e + 15$ |
59 | $[59, 59, -3w^{5} + 2w^{4} + 18w^{3} - 15w^{2} - 14w + 7]$ | $\phantom{-}3e^{7} - \frac{17}{2}e^{6} - 42e^{5} + 80e^{4} + \frac{415}{2}e^{3} - 135e^{2} - \frac{557}{2}e - \frac{65}{2}$ |
59 | $[59, 59, 2w^{5} - 12w^{3} + 3w^{2} + 12w - 3]$ | $-\frac{3}{2}e^{7} + \frac{9}{2}e^{6} + 20e^{5} - \frac{83}{2}e^{4} - \frac{193}{2}e^{3} + \frac{139}{2}e^{2} + 128e + \frac{35}{2}$ |
59 | $[59, 59, -2w^{5} + w^{4} + 12w^{3} - 8w^{2} - 11w + 3]$ | $-\frac{1}{4}e^{7} + \frac{1}{4}e^{6} + \frac{11}{2}e^{5} - \frac{13}{4}e^{4} - \frac{133}{4}e^{3} + \frac{7}{4}e^{2} + 46e + \frac{45}{4}$ |
61 | $[61, 61, -4w^{5} + 2w^{4} + 24w^{3} - 16w^{2} - 19w + 8]$ | $-\frac{5}{2}e^{7} + 7e^{6} + \frac{71}{2}e^{5} - 67e^{4} - \frac{353}{2}e^{3} + \frac{239}{2}e^{2} + \frac{475}{2}e + \frac{29}{2}$ |
61 | $[61, 61, 5w^{5} - 3w^{4} - 31w^{3} + 22w^{2} + 27w - 13]$ | $\phantom{-}\frac{9}{2}e^{7} - \frac{25}{2}e^{6} - 64e^{5} + \frac{237}{2}e^{4} + \frac{639}{2}e^{3} - \frac{409}{2}e^{2} - 432e - \frac{71}{2}$ |
61 | $[61, 61, 3w^{5} - w^{4} - 18w^{3} + 9w^{2} + 16w - 4]$ | $-\frac{11}{4}e^{7} + \frac{31}{4}e^{6} + \frac{77}{2}e^{5} - \frac{291}{4}e^{4} - \frac{755}{4}e^{3} + \frac{481}{4}e^{2} + 249e + \frac{123}{4}$ |
71 | $[71, 71, 2w^{5} - 12w^{3} + 2w^{2} + 11w - 1]$ | $\phantom{-}\frac{19}{4}e^{7} - \frac{55}{4}e^{6} - \frac{131}{2}e^{5} + \frac{523}{4}e^{4} + \frac{1271}{4}e^{3} - \frac{937}{4}e^{2} - 418e - \frac{87}{4}$ |
71 | $[71, 71, 3w^{5} - 2w^{4} - 18w^{3} + 15w^{2} + 13w - 9]$ | $-\frac{1}{2}e^{7} + \frac{3}{2}e^{6} + 7e^{5} - \frac{31}{2}e^{4} - \frac{69}{2}e^{3} + \frac{73}{2}e^{2} + 50e - \frac{21}{2}$ |
71 | $[71, 71, -w^{5} + w^{4} + 6w^{3} - 7w^{2} - 6w + 5]$ | $-\frac{9}{2}e^{7} + \frac{25}{2}e^{6} + 64e^{5} - \frac{237}{2}e^{4} - \frac{637}{2}e^{3} + \frac{409}{2}e^{2} + 425e + \frac{59}{2}$ |
79 | $[79, 79, -w^{5} + 7w^{3} - w^{2} - 10w]$ | $-2e^{7} + \frac{11}{2}e^{6} + 28e^{5} - 50e^{4} - \frac{277}{2}e^{3} + 74e^{2} + \frac{369}{2}e + \frac{65}{2}$ |
79 | $[79, 79, 4w^{5} - 2w^{4} - 25w^{3} + 15w^{2} + 23w - 9]$ | $\phantom{-}\frac{11}{2}e^{7} - 16e^{6} - \frac{151}{2}e^{5} + 152e^{4} + \frac{731}{2}e^{3} - \frac{545}{2}e^{2} - \frac{967}{2}e - \frac{55}{2}$ |
79 | $[79, 79, -w^{5} + 6w^{3} - 2w^{2} - 7w + 4]$ | $-\frac{13}{4}e^{7} + \frac{37}{4}e^{6} + \frac{91}{2}e^{5} - \frac{349}{4}e^{4} - \frac{901}{4}e^{3} + \frac{591}{4}e^{2} + 304e + \frac{165}{4}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$49$ | $[49, 7, -3w^{5} + 2w^{4} + 19w^{3} - 15w^{2} - 19w + 9]$ | $1$ |