Properties

Label 2.2.120.1-14.2-e
Base field \(\Q(\sqrt{30}) \)
Weight $[2, 2]$
Level norm $14$
Level $[14,14,w - 4]$
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: $[14,14,w - 4]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $32$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 23x^{2} + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{24}{5}e$
3 $[3, 3, w]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{24}{5}e$
5 $[5, 5, -w + 5]$ $\phantom{-}1$
7 $[7, 7, w + 3]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{24}{5}e$
7 $[7, 7, w + 4]$ $\phantom{-}e$
13 $[13, 13, w + 2]$ $\phantom{-}\frac{7}{5}e^{3} + \frac{158}{5}e$
13 $[13, 13, w + 11]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{24}{5}e$
17 $[17, 17, w + 8]$ $\phantom{-}e$
17 $[17, 17, w + 9]$ $\phantom{-}\frac{4}{5}e^{3} + \frac{86}{5}e$
19 $[19, 19, w + 7]$ $-\frac{1}{5}e^{2} - \frac{14}{5}$
19 $[19, 19, -w + 7]$ $-\frac{1}{5}e^{2} + \frac{11}{5}$
29 $[29, 29, -w - 1]$ $\phantom{-}\frac{2}{5}e^{2} + \frac{28}{5}$
29 $[29, 29, w - 1]$ $-5$
37 $[37, 37, w + 17]$ $-\frac{6}{5}e^{3} - \frac{129}{5}e$
37 $[37, 37, w + 20]$ $\phantom{-}\frac{9}{5}e^{3} + \frac{206}{5}e$
71 $[71, 71, 2w - 7]$ $-\frac{1}{5}e^{2} - \frac{29}{5}$
71 $[71, 71, -2w - 7]$ $\phantom{-}\frac{1}{5}e^{2} + \frac{49}{5}$
83 $[83, 83, w + 14]$ $-\frac{11}{5}e^{3} - \frac{244}{5}e$
83 $[83, 83, w + 69]$ $-\frac{9}{5}e^{3} - \frac{216}{5}e$
101 $[101, 101, -7w + 37]$ $-\frac{3}{5}e^{2} - \frac{32}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,-w]$ $-\frac{1}{5}e^{3} - \frac{24}{5}e$
$7$ $[7,7,-w + 4]$ $-\frac{1}{5}e^{3} - \frac{24}{5}e$