Properties

Label 2.2.60.1-11.2-f
Base field \(\Q(\sqrt{15}) \)
Weight $[2, 2]$
Level norm $11$
Level $[11,11,w - 2]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{15}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 15\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[11,11,w - 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $-e^{3} - 5e$
5 $[5, 5, w]$ $\phantom{-}e^{3} + 3e$
7 $[7, 7, w + 1]$ $-2e$
7 $[7, 7, w + 6]$ $\phantom{-}e^{3} + 5e$
11 $[11, 11, -w - 2]$ $\phantom{-}4$
11 $[11, 11, w - 2]$ $-1$
17 $[17, 17, w + 7]$ $\phantom{-}3e^{3} + 13e$
17 $[17, 17, w + 10]$ $-2e^{3} - 6e$
43 $[43, 43, w + 12]$ $-6e$
43 $[43, 43, w + 31]$ $\phantom{-}e^{3} + e$
53 $[53, 53, w + 11]$ $-4e^{3} - 16e$
53 $[53, 53, w + 42]$ $-4e^{3} - 16e$
59 $[59, 59, 2w - 1]$ $\phantom{-}2e^{2} + 2$
59 $[59, 59, -2w - 1]$ $-2e^{2} - 10$
61 $[61, 61, 2w - 11]$ $-2$
61 $[61, 61, -2w - 11]$ $-4e^{2} - 14$
67 $[67, 67, w + 22]$ $-2e^{3} - 12e$
67 $[67, 67, w + 45]$ $\phantom{-}2e^{3} + 16e$
71 $[71, 71, 3w - 8]$ $-8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11,11,w - 2]$ $1$