Properties

Label 3.3.961.1-4.5-a
Base field 3.3.961.1
Weight $[2, 2, 2]$
Level norm $4$
Level $[4,4,-w + 3]$
Dimension $3$
CM no
Base change no

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Base field 3.3.961.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 8\); narrow class number \(1\) and class number \(1\).

Form

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

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + x^{2} - 3x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{2} - \frac{1}{2}w - 4]$ $\phantom{-}e$
2 $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 3]$ $\phantom{-}e^{2} + e - 1$
2 $[2, 2, -w + 1]$ $\phantom{-}0$
23 $[23, 23, -w^{2} + w + 7]$ $-2e^{2} - 2e + 4$
23 $[23, 23, w^{2} + w - 7]$ $-2e - 2$
23 $[23, 23, -2w + 1]$ $-2e^{2} - 2e + 8$
27 $[27, 3, 3]$ $-e^{2} - 4e + 3$
29 $[29, 29, -w^{2} - 3w + 1]$ $\phantom{-}e^{2} + 2e + 3$
29 $[29, 29, w^{2} - 3w + 1]$ $\phantom{-}e^{2} - 1$
29 $[29, 29, -2w^{2} + 21]$ $-e^{2} - 3$
31 $[31, 31, -3w^{2} + w + 31]$ $-e^{2} - 4e - 1$
47 $[47, 47, 2w - 3]$ $\phantom{-}2e^{2} - 4e - 6$
47 $[47, 47, w^{2} + w - 5]$ $\phantom{-}2e^{2} - 6$
47 $[47, 47, w^{2} - w - 9]$ $-2e^{2} + 2$
61 $[61, 61, w^{2} - w - 11]$ $\phantom{-}7e^{2} + 6e - 11$
61 $[61, 61, -w^{2} - w + 3]$ $-e^{2} + 4e + 9$
61 $[61, 61, -2w + 5]$ $-3e^{2} - 4e + 7$
89 $[89, 89, w^{2} - w - 1]$ $\phantom{-}3e^{2} - 6e - 13$
89 $[89, 89, w^{2} + w - 13]$ $-e^{2} + 4e + 11$
89 $[89, 89, -2w - 5]$ $\phantom{-}5e^{2} + 6e - 15$
Display number of eigenvalues

Atkin-Lehner eigenvalues

The Atkin-Lehner eigenvalues for this form are not in the database.