Properties

Base field \(\Q(\sqrt{113}) \)
Weight [2, 2]
Level norm 8
Level $[8, 8, -w + 5]$
Label 2.2.113.1-8.3-c
Dimension 6
CM no
Base change no

Related objects

Downloads

Learn more about

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 $[8, 8, -w + 5]$
Label 2.2.113.1-8.3-c
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut -\mathstrut 10x^{4} \) \(\mathstrut +\mathstrut 7x^{3} \) \(\mathstrut +\mathstrut 22x^{2} \) \(\mathstrut -\mathstrut 2x \) \(\mathstrut -\mathstrut 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}e$
2 $[2, 2, w + 5]$ $\phantom{-}0$
7 $[7, 7, 6w - 35]$ $-\frac{1}{2}e^{5} + 5e^{3} + \frac{1}{2}e^{2} - \frac{21}{2}e - \frac{5}{2}$
7 $[7, 7, -6w - 29]$ $-e^{5} + e^{4} + 9e^{3} - 7e^{2} - 16e + 2$
9 $[9, 3, 3]$ $-\frac{1}{2}e^{5} + e^{4} + 5e^{3} - \frac{13}{2}e^{2} - \frac{23}{2}e + \frac{1}{2}$
11 $[11, 11, 4w + 19]$ $\phantom{-}e^{3} + e^{2} - 7e - 3$
11 $[11, 11, 4w - 23]$ $\phantom{-}\frac{1}{2}e^{5} - e^{4} - 5e^{3} + \frac{13}{2}e^{2} + \frac{21}{2}e + \frac{1}{2}$
13 $[13, 13, -2w + 11]$ $-e^{5} + e^{4} + 10e^{3} - 7e^{2} - 22e + 3$
13 $[13, 13, 2w + 9]$ $-\frac{1}{2}e^{5} + 4e^{3} + \frac{1}{2}e^{2} - \frac{9}{2}e - \frac{7}{2}$
25 $[25, 5, -5]$ $\phantom{-}e^{3} - 5e - 2$
31 $[31, 31, 2w - 13]$ $-e^{5} + e^{4} + 10e^{3} - 7e^{2} - 23e$
31 $[31, 31, -2w - 11]$ $\phantom{-}\frac{3}{2}e^{5} - 14e^{3} + \frac{1}{2}e^{2} + \frac{53}{2}e + \frac{3}{2}$
41 $[41, 41, -8w - 39]$ $-e^{5} + 2e^{4} + 12e^{3} - 13e^{2} - 34e + 2$
41 $[41, 41, 8w - 47]$ $-2e^{2} + e + 9$
53 $[53, 53, -26w - 125]$ $-e^{5} + 8e^{3} - e^{2} - 12e + 6$
53 $[53, 53, 26w - 151]$ $\phantom{-}\frac{3}{2}e^{5} - e^{4} - 14e^{3} + \frac{17}{2}e^{2} + \frac{47}{2}e - \frac{13}{2}$
61 $[61, 61, -14w + 81]$ $-e^{5} + 10e^{3} + 2e^{2} - 25e - 8$
61 $[61, 61, -14w - 67]$ $\phantom{-}e^{5} - 10e^{3} + 25e + 2$
83 $[83, 83, 2w - 15]$ $-\frac{3}{2}e^{5} + 14e^{3} - \frac{3}{2}e^{2} - \frac{53}{2}e + \frac{7}{2}$
83 $[83, 83, -2w - 13]$ $-e^{5} + e^{4} + 8e^{3} - 6e^{2} - 9e + 7$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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