Properties

Label 2.2.157.1-16.1-c
Base field \(\Q(\sqrt{157}) \)
Weight $[2, 2]$
Level norm $16$
Level $[16, 4, 4]$
Dimension $5$
CM no
Base change yes

Related objects

Downloads

Learn more

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: $[16, 4, 4]$
Dimension: $5$
CM: no
Base change: yes
Newspace dimension: $36$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} + 3x^{4} - 5x^{3} - 19x^{2} - 10x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $\phantom{-}e$
3 $[3, 3, -w + 7]$ $\phantom{-}e$
4 $[4, 2, 2]$ $\phantom{-}0$
11 $[11, 11, -3w - 17]$ $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 12e$
11 $[11, 11, 3w - 20]$ $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 12e$
13 $[13, 13, 2w - 13]$ $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 13e - 3$
13 $[13, 13, 2w + 11]$ $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 13e - 3$
17 $[17, 17, w + 7]$ $-e^{4} - e^{3} + 7e^{2} + 6e - 2$
17 $[17, 17, -w + 8]$ $-e^{4} - e^{3} + 7e^{2} + 6e - 2$
19 $[19, 19, -w - 4]$ $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 11e - 1$
19 $[19, 19, -w + 5]$ $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 11e - 1$
25 $[25, 5, 5]$ $-e^{2} - e + 5$
31 $[31, 31, -6w - 35]$ $\phantom{-}e^{4} + 3e^{3} - 6e^{2} - 17e - 4$
31 $[31, 31, -6w + 41]$ $\phantom{-}e^{4} + 3e^{3} - 6e^{2} - 17e - 4$
37 $[37, 37, -w - 1]$ $\phantom{-}e^{4} - 8e^{2} + 6$
37 $[37, 37, w - 2]$ $\phantom{-}e^{4} - 8e^{2} + 6$
47 $[47, 47, 3w + 16]$ $\phantom{-}e^{3} + e^{2} - 8e - 8$
47 $[47, 47, -3w + 19]$ $\phantom{-}e^{3} + e^{2} - 8e - 8$
49 $[49, 7, -7]$ $-e^{4} - e^{3} + 6e^{2} + 9e + 10$
67 $[67, 67, 3w - 22]$ $\phantom{-}e^{4} - 8e^{2} + 4e + 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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