Properties

Label 6.6.722000.1-49.1-e
Base field 6.6.722000.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $49$
Level $[49, 7, -3w^{5} + 2w^{4} + 19w^{3} - 15w^{2} - 19w + 9]$
Dimension $8$
CM no
Base change no

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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 $[79, 79, -w^{5} + 6w^{3} - 2w^{2} - 7w + 4]$ $-\frac{13}{4}e^{7} + \frac{37}{4}e^{6} + \frac{91}{2}e^{5} - \frac{349}{4}e^{4} - \frac{901}{4}e^{3} + \frac{591}{4}e^{2} + 304e + \frac{165}{4}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$49$ $[49, 7, -3w^{5} + 2w^{4} + 19w^{3} - 15w^{2} - 19w + 9]$ $1$