Properties

Label 2.2.56.1-13.1-a
Base field \(\Q(\sqrt{14}) \)
Weight $[2, 2]$
Level norm $13$
Level $[13, 13, -w - 1]$
Dimension $5$
CM no
Base change no

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Base field \(\Q(\sqrt{14}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 14\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[13, 13, -w - 1]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - x^{4} - 7x^{3} + 6x^{2} + 7x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 4]$ $\phantom{-}e$
5 $[5, 5, -w + 3]$ $-e^{3} - e^{2} + 6e + 3$
5 $[5, 5, w + 3]$ $-e^{4} + 2e^{3} + 7e^{2} - 11e - 4$
7 $[7, 7, -2w - 7]$ $\phantom{-}e^{4} - 6e^{2} + 2e + 3$
9 $[9, 3, 3]$ $-2e^{4} + 2e^{3} + 12e^{2} - 13e - 7$
11 $[11, 11, w + 5]$ $\phantom{-}e^{4} - 2e^{3} - 8e^{2} + 12e + 7$
11 $[11, 11, -w + 5]$ $\phantom{-}e^{3} - 5e$
13 $[13, 13, -w - 1]$ $-1$
13 $[13, 13, -w + 1]$ $-2e^{4} + e^{3} + 12e^{2} - 9e - 2$
31 $[31, 31, 2w - 5]$ $\phantom{-}4e^{4} - 5e^{3} - 26e^{2} + 32e + 16$
31 $[31, 31, -2w - 5]$ $\phantom{-}e^{4} - 3e^{3} - 7e^{2} + 15e + 8$
43 $[43, 43, 7w + 27]$ $\phantom{-}3e^{4} - 3e^{3} - 17e^{2} + 17e + 5$
43 $[43, 43, 3w + 13]$ $\phantom{-}2e^{4} - e^{3} - 12e^{2} + 11e + 5$
47 $[47, 47, 2w - 3]$ $\phantom{-}e^{4} - 9e^{2} - e + 9$
47 $[47, 47, -2w - 3]$ $-e^{4} + e^{3} + 5e^{2} - 4e + 6$
61 $[61, 61, 7w + 25]$ $\phantom{-}e^{4} - e^{3} - 2e^{2} + 5e - 10$
61 $[61, 61, -5w - 17]$ $\phantom{-}3e^{4} - e^{3} - 18e^{2} + 10e + 13$
67 $[67, 67, -w - 9]$ $-2e^{4} + e^{3} + 13e^{2} - 9e - 13$
67 $[67, 67, w - 9]$ $\phantom{-}5e^{4} - 7e^{3} - 33e^{2} + 41e + 19$
101 $[101, 101, 3w - 5]$ $\phantom{-}3e^{3} + e^{2} - 20e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w - 1]$ $1$