Properties

Label 2.2.120.1-14.1-c
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:

\(x^{4} - x^{3} - 6x^{2} + x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, -w + 5]$ $\phantom{-}e^{3} - e^{2} - 6e - 1$
7 $[7, 7, w + 3]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 3e + \frac{3}{2}$
7 $[7, 7, w + 4]$ $\phantom{-}1$
13 $[13, 13, w + 2]$ $\phantom{-}e^{3} - 7e - 1$
13 $[13, 13, w + 11]$ $-e^{3} + e^{2} + 4e + 1$
17 $[17, 17, w + 8]$ $-e^{3} + 8e + 1$
17 $[17, 17, w + 9]$ $-\frac{1}{2}e^{3} + 2e^{2} - \frac{11}{2}$
19 $[19, 19, w + 7]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 2e + \frac{1}{2}$
19 $[19, 19, -w + 7]$ $-\frac{5}{2}e^{3} + 2e^{2} + 15e - \frac{3}{2}$
29 $[29, 29, -w - 1]$ $\phantom{-}e^{3} - e^{2} - 5e - 4$
29 $[29, 29, w - 1]$ $-3e^{3} + 3e^{2} + 16e - 2$
37 $[37, 37, w + 17]$ $-e^{2} + e + 7$
37 $[37, 37, w + 20]$ $\phantom{-}\frac{5}{2}e^{3} - 3e^{2} - 12e + \frac{5}{2}$
71 $[71, 71, 2w - 7]$ $\phantom{-}\frac{7}{2}e^{3} - 3e^{2} - 22e + \frac{3}{2}$
71 $[71, 71, -2w - 7]$ $\phantom{-}\frac{3}{2}e^{3} - 3e^{2} - 8e - \frac{5}{2}$
83 $[83, 83, w + 14]$ $-3e^{3} + e^{2} + 15e + 6$
83 $[83, 83, w + 69]$ $-3e^{3} + e^{2} + 23e + 4$
101 $[101, 101, -7w + 37]$ $-\frac{5}{2}e^{3} + 5e^{2} + 8e - \frac{25}{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $1$
$7$ $[7, 7, w + 4]$ $-1$