Properties

Label 2.2.476.1-4.1-c
Base field \(\Q(\sqrt{119}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 2, 2]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{119}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 119\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[4, 2, 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $40$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 6x^{3} - 13x^{2} + 66x + 61\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 11]$ $\phantom{-}0$
5 $[5, 5, w + 2]$ $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{18}{43}e + \frac{105}{43}$
5 $[5, 5, w + 3]$ $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{18}{43}e + \frac{105}{43}$
7 $[7, 7, w]$ $\phantom{-}0$
9 $[9, 3, 3]$ $-\frac{6}{43}e^{3} + \frac{27}{43}e^{2} + \frac{54}{43}e - \frac{229}{43}$
11 $[11, 11, w + 3]$ $-\frac{2}{43}e^{3} + \frac{9}{43}e^{2} + \frac{61}{43}e - \frac{105}{43}$
11 $[11, 11, w + 8]$ $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{61}{43}e + \frac{105}{43}$
17 $[17, 17, w]$ $-\frac{8}{43}e^{3} + \frac{36}{43}e^{2} + \frac{72}{43}e - \frac{162}{43}$
19 $[19, 19, w - 10]$ $-\frac{1}{43}e^{3} + \frac{26}{43}e^{2} - \frac{34}{43}e - \frac{289}{43}$
19 $[19, 19, -w - 10]$ $\phantom{-}\frac{1}{43}e^{3} - \frac{26}{43}e^{2} + \frac{34}{43}e + \frac{289}{43}$
23 $[23, 23, w + 2]$ $-\frac{1}{43}e^{3} + \frac{26}{43}e^{2} - \frac{34}{43}e - \frac{289}{43}$
23 $[23, 23, w + 21]$ $\phantom{-}\frac{1}{43}e^{3} - \frac{26}{43}e^{2} + \frac{34}{43}e + \frac{289}{43}$
41 $[41, 41, w + 18]$ $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{18}{43}e - \frac{24}{43}$
41 $[41, 41, w + 23]$ $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{18}{43}e - \frac{24}{43}$
47 $[47, 47, -3w + 32]$ $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{61}{43}e + \frac{105}{43}$
47 $[47, 47, 8w - 87]$ $-\frac{2}{43}e^{3} + \frac{9}{43}e^{2} + \frac{61}{43}e - \frac{105}{43}$
53 $[53, 53, -2w + 23]$ $-\frac{6}{43}e^{3} + \frac{27}{43}e^{2} + \frac{54}{43}e - \frac{57}{43}$
53 $[53, 53, -13w + 142]$ $-\frac{6}{43}e^{3} + \frac{27}{43}e^{2} + \frac{54}{43}e - \frac{57}{43}$
59 $[59, 59, -5w + 54]$ $-\frac{4}{43}e^{3} + \frac{18}{43}e^{2} + \frac{122}{43}e - \frac{210}{43}$
59 $[59, 59, 6w - 65]$ $\phantom{-}\frac{4}{43}e^{3} - \frac{18}{43}e^{2} - \frac{122}{43}e + \frac{210}{43}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 11]$ $-1$