Properties

Base field 6.6.1241125.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 45
Level $[45, 15, 2w^{5} - 14w^{3} - 3w^{2} + 23w + 9]$
Label 6.6.1241125.1-45.1-k
Dimension 6
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 $[45, 15, 2w^{5} - 14w^{3} - 3w^{2} + 23w + 9]$
Label 6.6.1241125.1-45.1-k
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 27

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 4x^{5} \) \(\mathstrut -\mathstrut 22x^{4} \) \(\mathstrut +\mathstrut 80x^{3} \) \(\mathstrut +\mathstrut 32x^{2} \) \(\mathstrut -\mathstrut 160x \) \(\mathstrut +\mathstrut 64\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $\phantom{-}1$
9 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $\phantom{-}1$
11 $[11, 11, w - 1]$ $\phantom{-}e$
25 $[25, 5, w^{3} + w^{2} - 4w - 3]$ $\phantom{-}\frac{1}{48}e^{5} - \frac{1}{8}e^{4} - \frac{11}{24}e^{3} + \frac{37}{12}e^{2} + e - \frac{16}{3}$
29 $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ $-\frac{1}{2}e^{2} + 8$
41 $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-\frac{1}{6}e^{5} + \frac{1}{2}e^{4} + \frac{25}{6}e^{3} - \frac{55}{6}e^{2} - 13e + \frac{32}{3}$
49 $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ $\phantom{-}\frac{1}{48}e^{5} - \frac{1}{8}e^{4} - \frac{11}{24}e^{3} + \frac{31}{12}e^{2} + e - \frac{10}{3}$
59 $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ $-\frac{1}{8}e^{5} + \frac{1}{2}e^{4} + \frac{11}{4}e^{3} - 9e^{2} - 5e + 10$
59 $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ $-\frac{5}{16}e^{5} + \frac{7}{8}e^{4} + \frac{63}{8}e^{3} - \frac{65}{4}e^{2} - 26e + 28$
61 $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ $\phantom{-}\frac{1}{24}e^{5} - \frac{1}{4}e^{4} - \frac{11}{12}e^{3} + \frac{17}{3}e^{2} + e - \frac{32}{3}$
61 $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ $\phantom{-}\frac{1}{24}e^{5} - \frac{17}{12}e^{3} - \frac{1}{3}e^{2} + 10e - \frac{8}{3}$
64 $[64, 2, 2]$ $\phantom{-}\frac{1}{48}e^{5} - \frac{11}{24}e^{3} - \frac{1}{6}e^{2} - e + \frac{5}{3}$
71 $[71, 71, w^{3} + w^{2} - 5w - 3]$ $-\frac{1}{4}e^{5} + \frac{3}{4}e^{4} + \frac{13}{2}e^{3} - \frac{29}{2}e^{2} - 27e + 26$
71 $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ $\phantom{-}\frac{1}{3}e^{5} - e^{4} - \frac{47}{6}e^{3} + \frac{107}{6}e^{2} + 20e - \frac{64}{3}$
79 $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ $\phantom{-}\frac{1}{6}e^{5} - \frac{1}{2}e^{4} - \frac{25}{6}e^{3} + \frac{26}{3}e^{2} + 13e - \frac{14}{3}$
81 $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ $\phantom{-}\frac{5}{48}e^{5} - \frac{3}{8}e^{4} - \frac{55}{24}e^{3} + \frac{83}{12}e^{2} + 6e - \frac{14}{3}$
89 $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ $-\frac{5}{24}e^{5} + \frac{1}{2}e^{4} + \frac{61}{12}e^{3} - \frac{47}{6}e^{2} - 16e + \frac{22}{3}$
89 $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ $\phantom{-}\frac{1}{12}e^{5} - \frac{1}{4}e^{4} - \frac{7}{3}e^{3} + \frac{29}{6}e^{2} + 14e - \frac{34}{3}$
89 $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ $-e + 8$
89 $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ $\phantom{-}\frac{1}{48}e^{5} + \frac{1}{8}e^{4} - \frac{23}{24}e^{3} - \frac{35}{12}e^{2} + 7e + \frac{26}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $-1$
9 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $-1$