Properties

Label 3.3.257.1-35.1-a
Base field 3.3.257.1
Weight $[2, 2, 2]$
Level norm $35$
Level $[35, 35, -w + 4]$
Dimension $3$
CM no
Base change no

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Base field 3.3.257.1

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

Form

Weight: $[2, 2, 2]$
Level: $[35, 35, -w + 4]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 2x^{2} - 5x + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $\phantom{-}1$
7 $[7, 7, -w^{2} + 2]$ $-1$
8 $[8, 2, 2]$ $-e^{2} + e + 5$
9 $[9, 3, -w^{2} + w + 4]$ $-e^{2} + 2e + 2$
19 $[19, 19, w^{2} + w - 4]$ $\phantom{-}e$
25 $[25, 5, -w^{2} + 2w + 2]$ $-2e + 2$
37 $[37, 37, 2w + 1]$ $\phantom{-}2e^{2} - 5e - 6$
41 $[41, 41, -2w^{2} - w + 7]$ $\phantom{-}2e^{2} - 4e - 6$
43 $[43, 43, -2w^{2} + 5]$ $-e$
47 $[47, 47, 3w - 4]$ $-e^{2} - 2e + 8$
49 $[49, 7, 2w^{2} - w - 5]$ $\phantom{-}2e - 6$
53 $[53, 53, -2w^{2} + 2w + 7]$ $\phantom{-}e^{2} - 10$
61 $[61, 61, -w^{2} - 3w + 4]$ $-2e + 6$
61 $[61, 61, 3w^{2} - w - 10]$ $\phantom{-}2e^{2} - 6e - 10$
61 $[61, 61, w^{2} - 2w - 4]$ $-3e + 10$
67 $[67, 67, 2w^{2} - w - 4]$ $\phantom{-}e^{2} - 12$
67 $[67, 67, 2w^{2} - w - 2]$ $\phantom{-}3e^{2} - 4e - 12$
67 $[67, 67, w^{2} + 2w - 5]$ $\phantom{-}4e^{2} - 4e - 12$
71 $[71, 71, -2w^{2} - w + 10]$ $-2e^{2} + 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w + 1]$ $-1$
$7$ $[7, 7, -w^{2} + 2]$ $1$