Properties

Base field 6.6.1241125.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 55
Level $[55, 55, w^{5} - 8w^{3} - 2w^{2} + 15w + 5]$
Label 6.6.1241125.1-55.1-h
Dimension 5
CM no
Base change no

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Base field 6.6.1241125.1

Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2, 2, 2]
Level $[55, 55, w^{5} - 8w^{3} - 2w^{2} + 15w + 5]$
Label 6.6.1241125.1-55.1-h
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 33

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} \) \(\mathstrut -\mathstrut 27x^{3} \) \(\mathstrut -\mathstrut 6x^{2} \) \(\mathstrut +\mathstrut 40x \) \(\mathstrut -\mathstrut 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $-1$
9 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $\phantom{-}e$
11 $[11, 11, w - 1]$ $\phantom{-}1$
25 $[25, 5, w^{3} + w^{2} - 4w - 3]$ $-e$
29 $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ $\phantom{-}\frac{5}{2}e^{4} + \frac{3}{2}e^{3} - \frac{133}{2}e^{2} - \frac{109}{2}e + 59$
41 $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}\frac{3}{4}e^{4} + \frac{1}{2}e^{3} - \frac{81}{4}e^{2} - 17e + 21$
49 $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ $-\frac{1}{2}e^{4} + \frac{27}{2}e^{2} + 2e - 16$
59 $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ $-\frac{5}{2}e^{4} - 2e^{3} + \frac{133}{2}e^{2} + 66e - 66$
59 $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ $-\frac{9}{4}e^{4} - \frac{3}{2}e^{3} + \frac{239}{4}e^{2} + 53e - 57$
61 $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ $\phantom{-}e^{4} + e^{3} - 27e^{2} - 31e + 24$
61 $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ $-\frac{3}{2}e^{4} - e^{3} + \frac{81}{2}e^{2} + 36e - 48$
64 $[64, 2, 2]$ $\phantom{-}\frac{9}{4}e^{4} + e^{3} - \frac{239}{4}e^{2} - \frac{87}{2}e + 59$
71 $[71, 71, w^{3} + w^{2} - 5w - 3]$ $\phantom{-}e^{4} + \frac{1}{2}e^{3} - 27e^{2} - \frac{39}{2}e + 25$
71 $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ $-\frac{7}{2}e^{4} - 2e^{3} + \frac{185}{2}e^{2} + 74e - 86$
79 $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ $-\frac{5}{4}e^{4} - \frac{1}{2}e^{3} + \frac{135}{4}e^{2} + 21e - 41$
81 $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ $\phantom{-}\frac{3}{2}e^{4} + \frac{1}{2}e^{3} - \frac{79}{2}e^{2} - \frac{47}{2}e + 41$
89 $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ $\phantom{-}\frac{7}{2}e^{4} + \frac{5}{2}e^{3} - \frac{187}{2}e^{2} - \frac{175}{2}e + 89$
89 $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ $\phantom{-}\frac{9}{4}e^{4} + \frac{3}{2}e^{3} - \frac{239}{4}e^{2} - 54e + 53$
89 $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ $-4e^{4} - \frac{5}{2}e^{3} + 106e^{2} + \frac{181}{2}e - 101$
89 $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ $-e^{4} - e^{3} + 27e^{2} + 31e - 32$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $1$
11 $[11, 11, w - 1]$ $-1$