Properties

Label 2.2.157.1-12.1-e
Base field \(\Q(\sqrt{157}) \)
Weight $[2, 2]$
Level norm $12$
Level $[12, 6, 2w + 12]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\sqrt{157}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[12, 6, 2w + 12]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $\phantom{-}1$
3 $[3, 3, -w + 7]$ $\phantom{-}e$
4 $[4, 2, 2]$ $\phantom{-}1$
11 $[11, 11, -3w - 17]$ $-4$
11 $[11, 11, 3w - 20]$ $-e + 4$
13 $[13, 13, 2w - 13]$ $\phantom{-}2e - 1$
13 $[13, 13, 2w + 11]$ $\phantom{-}3$
17 $[17, 17, w + 7]$ $\phantom{-}e - 1$
17 $[17, 17, -w + 8]$ $-e + 3$
19 $[19, 19, -w - 4]$ $\phantom{-}4$
19 $[19, 19, -w + 5]$ $\phantom{-}e - 4$
25 $[25, 5, 5]$ $-2e + 2$
31 $[31, 31, -6w - 35]$ $\phantom{-}3e$
31 $[31, 31, -6w + 41]$ $-4e - 4$
37 $[37, 37, -w - 1]$ $\phantom{-}e + 7$
37 $[37, 37, w - 2]$ $-9$
47 $[47, 47, 3w + 16]$ $\phantom{-}4$
47 $[47, 47, -3w + 19]$ $\phantom{-}2e + 4$
49 $[49, 7, -7]$ $-3e + 3$
67 $[67, 67, 3w - 22]$ $\phantom{-}2e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 6]$ $-1$
$4$ $[4, 2, 2]$ $-1$