Properties

Label 2.2.113.1-16.1-a
Base field \(\Q(\sqrt{113}) \)
Weight $[2, 2]$
Level norm $16$
Level $[16, 4, 4]$
Dimension $5$
CM no
Base change yes

Related objects

Downloads

Learn more

Base field \(\Q(\sqrt{113}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); 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: $5$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - 21x^{3} - 17x^{2} + 96x + 120\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}0$
2 $[2, 2, w + 5]$ $\phantom{-}0$
7 $[7, 7, 6w - 35]$ $\phantom{-}e$
7 $[7, 7, -6w - 29]$ $\phantom{-}e$
9 $[9, 3, 3]$ $-\frac{1}{2}e^{4} + e^{3} + \frac{17}{2}e^{2} - \frac{15}{2}e - 30$
11 $[11, 11, 4w + 19]$ $-e^{2} + e + 8$
11 $[11, 11, 4w - 23]$ $-e^{2} + e + 8$
13 $[13, 13, -2w + 11]$ $-\frac{1}{6}e^{4} + \frac{2}{3}e^{3} + \frac{11}{6}e^{2} - \frac{11}{2}e - 6$
13 $[13, 13, 2w + 9]$ $-\frac{1}{6}e^{4} + \frac{2}{3}e^{3} + \frac{11}{6}e^{2} - \frac{11}{2}e - 6$
25 $[25, 5, -5]$ $-\frac{1}{3}e^{4} + \frac{1}{3}e^{3} + \frac{17}{3}e^{2} - 2e - 14$
31 $[31, 31, 2w - 13]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{17}{3}e^{2} + e + 20$
31 $[31, 31, -2w - 11]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{17}{3}e^{2} + e + 20$
41 $[41, 41, -8w - 39]$ $-\frac{1}{2}e^{4} + e^{3} + \frac{15}{2}e^{2} - \frac{13}{2}e - 26$
41 $[41, 41, 8w - 47]$ $-\frac{1}{2}e^{4} + e^{3} + \frac{15}{2}e^{2} - \frac{13}{2}e - 26$
53 $[53, 53, -26w - 125]$ $-\frac{1}{2}e^{4} + e^{3} + \frac{19}{2}e^{2} - \frac{17}{2}e - 42$
53 $[53, 53, 26w - 151]$ $-\frac{1}{2}e^{4} + e^{3} + \frac{19}{2}e^{2} - \frac{17}{2}e - 42$
61 $[61, 61, -14w + 81]$ $\phantom{-}\frac{2}{3}e^{4} - \frac{5}{3}e^{3} - \frac{31}{3}e^{2} + 12e + 40$
61 $[61, 61, -14w - 67]$ $\phantom{-}\frac{2}{3}e^{4} - \frac{5}{3}e^{3} - \frac{31}{3}e^{2} + 12e + 40$
83 $[83, 83, 2w - 15]$ $\phantom{-}e^{4} - 2e^{3} - 18e^{2} + 19e + 76$
83 $[83, 83, -2w - 13]$ $\phantom{-}e^{4} - 2e^{3} - 18e^{2} + 19e + 76$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 6]$ $-1$
$2$ $[2, 2, w + 5]$ $-1$