Properties

Base field \(\Q(\sqrt{157}) \)
Weight [2, 2]
Level norm 4
Level $[4, 2, 2]$
Label 2.2.157.1-4.1-a
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 $[4, 2, 2]$
Label 2.2.157.1-4.1-a
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 11

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut -\mathstrut x \) \(\mathstrut -\mathstrut 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $\phantom{-}e$
3 $[3, 3, -w + 7]$ $-e + 1$
4 $[4, 2, 2]$ $-1$
11 $[11, 11, -3w - 17]$ $\phantom{-}e + 3$
11 $[11, 11, 3w - 20]$ $-e + 4$
13 $[13, 13, 2w - 13]$ $-e + 3$
13 $[13, 13, 2w + 11]$ $\phantom{-}e + 2$
17 $[17, 17, w + 7]$ $-e + 2$
17 $[17, 17, -w + 8]$ $\phantom{-}e + 1$
19 $[19, 19, -w - 4]$ $\phantom{-}e - 3$
19 $[19, 19, -w + 5]$ $-e - 2$
25 $[25, 5, 5]$ $-5$
31 $[31, 31, -6w - 35]$ $-e - 4$
31 $[31, 31, -6w + 41]$ $\phantom{-}e - 5$
37 $[37, 37, -w - 1]$ $-2e + 2$
37 $[37, 37, w - 2]$ $\phantom{-}2e$
47 $[47, 47, 3w + 16]$ $-e + 3$
47 $[47, 47, -3w + 19]$ $\phantom{-}e + 2$
49 $[49, 7, -7]$ $-2$
67 $[67, 67, 3w - 22]$ $-e - 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $1$