Properties

Base field \(\Q(\sqrt{113}) \)
Weight [2, 2]
Level norm 7
Level $[7, 7, 6w - 35]$
Label 2.2.113.1-7.1-b
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 $[7, 7, 6w - 35]$
Label 2.2.113.1-7.1-b
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 17

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut -\mathstrut 9x^{4} \) \(\mathstrut +\mathstrut 9x^{3} \) \(\mathstrut +\mathstrut 14x^{2} \) \(\mathstrut -\mathstrut 9x \) \(\mathstrut -\mathstrut 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}e$
2 $[2, 2, w + 5]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{2}{7}e^{4} - \frac{10}{7}e^{3} - 2e^{2} + 3e + \frac{12}{7}$
7 $[7, 7, 6w - 35]$ $\phantom{-}1$
7 $[7, 7, -6w - 29]$ $-\frac{2}{7}e^{5} + \frac{3}{7}e^{4} + \frac{20}{7}e^{3} - 3e^{2} - 6e - \frac{3}{7}$
9 $[9, 3, 3]$ $-\frac{3}{7}e^{5} + \frac{1}{7}e^{4} + \frac{23}{7}e^{3} - 2e^{2} - 4e + \frac{13}{7}$
11 $[11, 11, 4w + 19]$ $-\frac{2}{7}e^{5} - \frac{4}{7}e^{4} + \frac{20}{7}e^{3} + 4e^{2} - 7e - \frac{24}{7}$
11 $[11, 11, 4w - 23]$ $-\frac{4}{7}e^{5} - \frac{1}{7}e^{4} + \frac{33}{7}e^{3} - 5e - \frac{6}{7}$
13 $[13, 13, -2w + 11]$ $-\frac{2}{7}e^{5} + \frac{3}{7}e^{4} + \frac{20}{7}e^{3} - 4e^{2} - 6e + \frac{18}{7}$
13 $[13, 13, 2w + 9]$ $\phantom{-}\frac{4}{7}e^{5} - \frac{6}{7}e^{4} - \frac{33}{7}e^{3} + 7e^{2} + 4e - \frac{36}{7}$
25 $[25, 5, -5]$ $\phantom{-}\frac{8}{7}e^{5} - \frac{5}{7}e^{4} - \frac{73}{7}e^{3} + 6e^{2} + 17e - \frac{51}{7}$
31 $[31, 31, 2w - 13]$ $-\frac{4}{7}e^{5} + \frac{6}{7}e^{4} + \frac{40}{7}e^{3} - 8e^{2} - 11e + \frac{43}{7}$
31 $[31, 31, -2w - 11]$ $-e^{2} + e + 1$
41 $[41, 41, -8w - 39]$ $\phantom{-}\frac{12}{7}e^{5} + \frac{3}{7}e^{4} - \frac{106}{7}e^{3} + 25e - \frac{31}{7}$
41 $[41, 41, 8w - 47]$ $\phantom{-}\frac{5}{7}e^{5} - \frac{4}{7}e^{4} - \frac{57}{7}e^{3} + 7e^{2} + 21e - \frac{66}{7}$
53 $[53, 53, -26w - 125]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{2}{7}e^{4} - \frac{10}{7}e^{3} - e^{2} + 4e - \frac{37}{7}$
53 $[53, 53, 26w - 151]$ $-\frac{3}{7}e^{5} + \frac{1}{7}e^{4} + \frac{37}{7}e^{3} - 14e - \frac{43}{7}$
61 $[61, 61, -14w + 81]$ $\phantom{-}e^{5} - 10e^{3} + e^{2} + 21e - 4$
61 $[61, 61, -14w - 67]$ $\phantom{-}e^{4} - 7e^{2} + 6e + 4$
83 $[83, 83, 2w - 15]$ $-\frac{19}{7}e^{5} + \frac{11}{7}e^{4} + \frac{162}{7}e^{3} - 15e^{2} - 30e + \frac{52}{7}$
83 $[83, 83, -2w - 13]$ $-\frac{5}{7}e^{5} + \frac{4}{7}e^{4} + \frac{57}{7}e^{3} - 3e^{2} - 23e - \frac{4}{7}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, 6w - 35]$ $-1$