Properties

Base field \(\Q(\sqrt{157}) \)
Weight [2, 2]
Level norm 16
Level $[16, 4, 4]$
Label 2.2.157.1-16.1-a
Dimension 1
CM no
Base change yes

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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 $[16, 4, 4]$
Label 2.2.157.1-16.1-a
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 36

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $\phantom{-}2$
3 $[3, 3, -w + 7]$ $\phantom{-}2$
4 $[4, 2, 2]$ $\phantom{-}0$
11 $[11, 11, -3w - 17]$ $\phantom{-}2$
11 $[11, 11, 3w - 20]$ $\phantom{-}2$
13 $[13, 13, 2w - 13]$ $\phantom{-}1$
13 $[13, 13, 2w + 11]$ $\phantom{-}1$
17 $[17, 17, w + 7]$ $\phantom{-}3$
17 $[17, 17, -w + 8]$ $\phantom{-}3$
19 $[19, 19, -w - 4]$ $-4$
19 $[19, 19, -w + 5]$ $-4$
25 $[25, 5, 5]$ $\phantom{-}10$
31 $[31, 31, -6w - 35]$ $\phantom{-}0$
31 $[31, 31, -6w + 41]$ $\phantom{-}0$
37 $[37, 37, -w - 1]$ $\phantom{-}1$
37 $[37, 37, w - 2]$ $\phantom{-}1$
47 $[47, 47, 3w + 16]$ $\phantom{-}10$
47 $[47, 47, -3w + 19]$ $\phantom{-}10$
49 $[49, 7, -7]$ $-5$
67 $[67, 67, 3w - 22]$ $-8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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