Properties

Label 3.3.1901.1-12.1-d
Base field 3.3.1901.1
Weight $[2, 2, 2]$
Level norm $12$
Level $[12, 6, w^{2} - 3w - 1]$
Dimension $7$
CM no
Base change no

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Base field 3.3.1901.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 4\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[12, 6, w^{2} - 3w - 1]$
Dimension: $7$
CM: no
Base change: no
Newspace dimension: $25$

Hecke eigenvalues ($q$-expansion)

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

\(x^{7} - 10x^{5} + 30x^{3} - x^{2} - 26x + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 2]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $-1$
4 $[4, 2, -w^{2} + 3w + 3]$ $-1$
9 $[9, 3, -w^{2} + 2w + 7]$ $-e^{3} + e^{2} + 4e - 4$
13 $[13, 13, w + 3]$ $-e^{5} + e^{4} + 8e^{3} - 6e^{2} - 15e + 7$
13 $[13, 13, -w + 3]$ $-e^{6} + e^{5} + 8e^{4} - 6e^{3} - 16e^{2} + 7e + 5$
13 $[13, 13, -w + 1]$ $-e^{5} + 8e^{3} - 2e^{2} - 14e + 5$
17 $[17, 17, -w^{2} - 2w + 1]$ $\phantom{-}e^{5} - 7e^{3} + e^{2} + 12e - 5$
23 $[23, 23, w^{2} - 2w - 5]$ $\phantom{-}e^{5} - e^{4} - 8e^{3} + 6e^{2} + 13e - 7$
31 $[31, 31, 2w + 3]$ $\phantom{-}e^{6} - 9e^{4} + 20e^{2} - 4$
31 $[31, 31, -2w^{2} + 3w + 15]$ $\phantom{-}e^{6} - 8e^{4} + 16e^{2} - e - 6$
31 $[31, 31, 3w + 7]$ $-e^{6} + 2e^{5} + 8e^{4} - 15e^{3} - 17e^{2} + 25e + 6$
37 $[37, 37, 3w^{2} - 4w - 27]$ $-e^{6} + 8e^{4} - 16e^{2} - e + 6$
41 $[41, 41, -2w^{2} + 7w + 1]$ $-2e^{5} + 14e^{3} + 2e^{2} - 22e - 6$
59 $[59, 59, w^{2} - 3]$ $\phantom{-}e^{6} - 9e^{4} + 22e^{2} - 2e - 12$
61 $[61, 61, 4w^{2} - 12w - 11]$ $\phantom{-}e^{6} - 2e^{5} - 10e^{4} + 12e^{3} + 26e^{2} - 13e - 6$
71 $[71, 71, w^{2} - 2w - 11]$ $-e^{6} - e^{5} + 7e^{4} + 6e^{3} - 12e^{2} - 6e + 5$
97 $[97, 97, 3w + 5]$ $\phantom{-}2e^{6} - 2e^{5} - 14e^{4} + 14e^{3} + 14e^{2} - 22e + 22$
101 $[101, 101, 2w^{2} - 6w - 7]$ $\phantom{-}e^{6} - 6e^{4} - 3e^{3} + 5e^{2} + 11e + 2$
103 $[103, 103, 2w^{2} - 3w - 19]$ $\phantom{-}e^{6} - 8e^{4} + e^{3} + 15e^{2} - e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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