Properties

Label 2.2.120.1-6.1-c
Base field \(\Q(\sqrt{30}) \)
Weight $[2, 2]$
Level norm $6$
Level $[6, 6, w - 6]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{30}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[6, 6, w - 6]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 26x^{2} + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}1$
3 $[3, 3, w]$ $\phantom{-}1$
5 $[5, 5, -w + 5]$ $-\frac{1}{12}e^{3} + \frac{11}{6}e$
7 $[7, 7, w + 3]$ $\phantom{-}e$
7 $[7, 7, w + 4]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{13}{2}e$
13 $[13, 13, w + 2]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{14}{3}e$
13 $[13, 13, w + 11]$ $-\frac{1}{12}e^{3} + \frac{17}{6}e$
17 $[17, 17, w + 8]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{10}{3}$
17 $[17, 17, w + 9]$ $-\frac{1}{3}e^{2} + \frac{16}{3}$
19 $[19, 19, w + 7]$ $-\frac{1}{3}e^{2} + \frac{22}{3}$
19 $[19, 19, -w + 7]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{4}{3}$
29 $[29, 29, -w - 1]$ $-\frac{5}{12}e^{3} + \frac{55}{6}e$
29 $[29, 29, w - 1]$ $-\frac{5}{12}e^{3} + \frac{55}{6}e$
37 $[37, 37, w + 17]$ $-\frac{1}{6}e^{3} + \frac{8}{3}e$
37 $[37, 37, w + 20]$ $-\frac{5}{12}e^{3} + \frac{61}{6}e$
71 $[71, 71, 2w - 7]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{50}{3}e$
71 $[71, 71, -2w - 7]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{5}{3}e$
83 $[83, 83, w + 14]$ $-\frac{1}{3}e^{2} + \frac{10}{3}$
83 $[83, 83, w + 69]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{16}{3}$
101 $[101, 101, -7w + 37]$ $-\frac{1}{2}e^{3} + 15e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-1$
$3$ $[3, 3, w]$ $-1$