Properties

Base field 3.3.761.1
Weight [2, 2, 2]
Level norm 11
Level $[11, 11, -w^{2} + 2w + 2]$
Label 3.3.761.1-11.1-b
Dimension 5
CM no
Base change no

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Base field 3.3.761.1

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

Form

Weight [2, 2, 2]
Level $[11, 11, -w^{2} + 2w + 2]$
Label 3.3.761.1-11.1-b
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 2x^{4} - 7x^{3} - 8x^{2} + 8x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 9e + 6$
8 $[8, 2, 2]$ $-\frac{4}{3}e^{4} - \frac{10}{3}e^{3} + \frac{23}{3}e^{2} + 14e - \frac{14}{3}$
9 $[9, 3, -w^{2} + 2w + 4]$ $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 8e + 1$
11 $[11, 11, -w^{2} + 2w + 2]$ $-1$
13 $[13, 13, -w^{2} + w + 4]$ $-e^{4} - 2e^{3} + 6e^{2} + 7e - 4$
19 $[19, 19, w + 3]$ $\phantom{-}\frac{1}{3}e^{4} + \frac{4}{3}e^{3} - \frac{5}{3}e^{2} - 5e + \frac{5}{3}$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}e^{2} + 2e - 3$
19 $[19, 19, -w^{2} + 3w + 2]$ $-\frac{4}{3}e^{4} - \frac{7}{3}e^{3} + \frac{26}{3}e^{2} + 8e - \frac{29}{3}$
23 $[23, 23, w^{2} - w - 3]$ $-\frac{5}{3}e^{4} - \frac{11}{3}e^{3} + \frac{31}{3}e^{2} + 16e - \frac{25}{3}$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}2e^{4} + 4e^{3} - 13e^{2} - 18e + 6$
23 $[23, 23, -w + 4]$ $\phantom{-}\frac{1}{3}e^{4} + \frac{4}{3}e^{3} + \frac{1}{3}e^{2} - 6e - \frac{16}{3}$
31 $[31, 31, w^{2} - 5]$ $\phantom{-}\frac{4}{3}e^{4} + \frac{13}{3}e^{3} - \frac{23}{3}e^{2} - 21e + \frac{20}{3}$
43 $[43, 43, w^{2} - 3w - 3]$ $\phantom{-}e^{4} + 3e^{3} - 4e^{2} - 14e$
49 $[49, 7, w^{2} - 6]$ $-\frac{7}{3}e^{4} - \frac{16}{3}e^{3} + \frac{41}{3}e^{2} + 19e - \frac{35}{3}$
53 $[53, 53, 2w - 5]$ $-\frac{10}{3}e^{4} - \frac{25}{3}e^{3} + \frac{59}{3}e^{2} + 38e - \frac{41}{3}$
61 $[61, 61, 2w^{2} - 2w - 9]$ $\phantom{-}2e^{4} + 4e^{3} - 13e^{2} - 13e + 13$
71 $[71, 71, 2w - 3]$ $\phantom{-}\frac{4}{3}e^{4} + \frac{7}{3}e^{3} - \frac{32}{3}e^{2} - 11e + \frac{20}{3}$
73 $[73, 73, 2w^{2} - 5w - 5]$ $-5e^{4} - 13e^{3} + 29e^{2} + 54e - 24$
83 $[83, 83, w^{2} - w - 9]$ $-\frac{1}{3}e^{4} + \frac{2}{3}e^{3} + \frac{8}{3}e^{2} - 5e - \frac{2}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w^{2} + 2w + 2]$ $1$