Properties

Label 4.4.5744.1-13.2-b
Base field 4.4.5744.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{2} + 3]$
Dimension $3$
CM no
Base change no

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Base field 4.4.5744.1

Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, -w^{2} + 3]$
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:

\(x^{3} + 2x^{2} - 9x - 19\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{3} + 4w + 1]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $-e^{2} + 5$
7 $[7, 7, -w^{2} + w + 2]$ $\phantom{-}e^{2} - e - 10$
13 $[13, 13, -w^{3} + w^{2} + 4w]$ $-e^{2} + 4$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}1$
17 $[17, 17, -w^{2} + 2]$ $\phantom{-}3e^{2} - 23$
19 $[19, 19, -w^{3} + 5w]$ $-5e^{2} + 2e + 38$
31 $[31, 31, -w^{2} + 2w + 3]$ $\phantom{-}e^{2} - 3e - 8$
37 $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ $\phantom{-}3e^{2} - 3e - 23$
43 $[43, 43, -w - 3]$ $\phantom{-}7e^{2} - 4e - 53$
53 $[53, 53, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}5e^{2} - 5e - 43$
53 $[53, 53, w^{3} - 6w - 2]$ $-2e^{2} + 13$
59 $[59, 59, 2w^{3} - w^{2} - 10w - 2]$ $-10e^{2} + 5e + 76$
61 $[61, 61, 2w^{3} - w^{2} - 10w]$ $-e^{2} + 3e + 11$
61 $[61, 61, 2w^{3} - w^{2} - 8w]$ $\phantom{-}e^{2} - e - 15$
71 $[71, 71, 2w^{3} - 9w - 2]$ $\phantom{-}3e^{2} - 28$
73 $[73, 73, -w^{3} - w^{2} + 6w + 3]$ $-3e - 5$
81 $[81, 3, -3]$ $-9e^{2} + 4e + 68$
83 $[83, 83, -w^{3} + 2w^{2} + 3w - 3]$ $-8e^{2} + e + 58$
101 $[101, 101, 2w^{3} - 8w - 3]$ $\phantom{-}6e^{2} - 5e - 53$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w^{2} + 3]$ $-1$