Properties

Label 3.3.985.1-23.1-a
Base field 3.3.985.1
Weight $[2, 2, 2]$
Level norm $23$
Level $[23, 23, -w^{2} + 3]$
Dimension $5$
CM no
Base change no

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Base field 3.3.985.1

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: $[23, 23, -w^{2} + 3]$
Dimension: $5$
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:

\(x^{5} - 12x^{3} + x^{2} + 4x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $-6e^{4} - 2e^{3} + 71e^{2} + 18e - 15$
7 $[7, 7, -w + 2]$ $\phantom{-}e^{4} - 12e^{2} + e + 6$
8 $[8, 2, 2]$ $-e + 1$
11 $[11, 11, -w^{2} + 2w + 2]$ $-2e^{4} + 24e^{2} - 2e - 5$
17 $[17, 17, -w - 3]$ $\phantom{-}8e^{4} + 3e^{3} - 95e^{2} - 27e + 25$
17 $[17, 17, -w^{2} + 2w + 1]$ $-4e^{4} - e^{3} + 48e^{2} + 8e - 12$
17 $[17, 17, -w^{2} + w + 4]$ $\phantom{-}2e^{4} - 24e^{2} + e + 6$
23 $[23, 23, -w^{2} + 3]$ $\phantom{-}1$
27 $[27, 3, -3]$ $-8e^{4} - 2e^{3} + 95e^{2} + 18e - 22$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}4e^{4} + e^{3} - 47e^{2} - 10e + 8$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}4e^{4} + e^{3} - 47e^{2} - 8e + 10$
29 $[29, 29, w^{2} - w - 1]$ $\phantom{-}11e^{4} + 4e^{3} - 131e^{2} - 35e + 35$
31 $[31, 31, w^{2} - 2]$ $\phantom{-}21e^{4} + 8e^{3} - 249e^{2} - 74e + 61$
37 $[37, 37, 2w - 5]$ $-12e^{4} - 5e^{3} + 142e^{2} + 48e - 35$
43 $[43, 43, w^{2} - 2w - 5]$ $-12e^{4} - 4e^{3} + 142e^{2} + 34e - 28$
47 $[47, 47, w^{2} - 3w - 2]$ $-16e^{4} - 6e^{3} + 190e^{2} + 56e - 41$
49 $[49, 7, w^{2} + w - 4]$ $\phantom{-}18e^{4} + 6e^{3} - 213e^{2} - 51e + 46$
53 $[53, 53, w^{2} - 2w - 6]$ $\phantom{-}13e^{4} + 4e^{3} - 155e^{2} - 36e + 38$
71 $[71, 71, w - 5]$ $-5e^{4} - 2e^{3} + 59e^{2} + 17e - 16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, -w^{2} + 3]$ $-1$