Properties

Label 6.6.1229312.1-41.3-c
Base field 6.6.1229312.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $41$
Level $[41,41,\frac{1}{4}w^{5} + \frac{1}{4}w^{4} - \frac{5}{2}w^{3} - 2w^{2} + 5w + 2]$
Dimension $3$
CM no
Base change no

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Base field 6.6.1229312.1

Generator \(w\), with minimal polynomial \(x^{6} - 10x^{4} + 24x^{2} - 8\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[41,41,\frac{1}{4}w^{5} + \frac{1}{4}w^{4} - \frac{5}{2}w^{3} - 2w^{2} + 5w + 2]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} + x^{2} - 5x + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + 2w^{3} + 2w^{2} - 3w - 3]$ $\phantom{-}e^{2} + 2e - 4$
7 $[7, 7, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + 2w^{3} - 2w^{2} - 3w + 3]$ $\phantom{-}e$
8 $[8, 2, -\frac{1}{4}w^{5} + 2w^{3} - 3w]$ $-e^{2} - e + 2$
41 $[41, 41, -\frac{1}{4}w^{4} - \frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 1]$ $\phantom{-}2e^{2} + 3e - 12$
41 $[41, 41, -\frac{1}{2}w^{2} - w + 2]$ $\phantom{-}2e^{2} + 2e - 8$
41 $[41, 41, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + 2w^{2} - 5w - 2]$ $\phantom{-}1$
41 $[41, 41, \frac{1}{4}w^{5} - \frac{1}{4}w^{4} - \frac{5}{2}w^{3} + 2w^{2} + 5w - 2]$ $\phantom{-}2$
41 $[41, 41, \frac{1}{2}w^{2} - w - 2]$ $-5e^{2} - 10e + 14$
41 $[41, 41, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 1]$ $-2e^{2} - 5e + 4$
71 $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + w^{2} - 5w + 1]$ $-2e^{2} + e + 8$
71 $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + \frac{3}{2}w^{2} - 6w - 2]$ $\phantom{-}4e^{2} + 4e - 8$
71 $[71, 71, \frac{1}{4}w^{4} - \frac{1}{2}w^{3} - \frac{5}{2}w^{2} + 3w + 4]$ $\phantom{-}2e^{2} + 2e - 4$
71 $[71, 71, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - 3w + 4]$ $\phantom{-}2e^{2} + 7e - 6$
71 $[71, 71, \frac{1}{2}w^{4} - \frac{7}{2}w^{2} + w + 3]$ $-4$
71 $[71, 71, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + \frac{5}{2}w^{3} - w^{2} - 5w - 1]$ $-4e^{2} - 10e + 14$
97 $[97, 97, \frac{1}{4}w^{5} - \frac{5}{2}w^{3} - \frac{1}{2}w^{2} + 5w]$ $-4e^{2} - 9e + 10$
97 $[97, 97, -\frac{1}{4}w^{4} + \frac{3}{2}w^{2} + w + 1]$ $\phantom{-}3e^{2} + 6e - 10$
97 $[97, 97, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + 2w^{2} - 3w - 4]$ $-4e^{2} - 10e + 18$
97 $[97, 97, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - 2w^{2} - 3w + 4]$ $\phantom{-}4e^{2} + 10e - 10$
97 $[97, 97, \frac{1}{4}w^{4} - \frac{3}{2}w^{2} + w - 1]$ $\phantom{-}4e^{2} + 10e - 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41,41,\frac{1}{4}w^{5} + \frac{1}{4}w^{4} - \frac{5}{2}w^{3} - 2w^{2} + 5w + 2]$ $-1$