Properties

Label 2.2.321.1-1.1-g
Base field \(\Q(\sqrt{321}) \)
Weight $[2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{321}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).

Form

Weight: $[2, 2]$
Level: $[1, 1, 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $69$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + x^{3} + 4x^{2} - 3x + 9\)

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Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
2 $[2, 2, w + 1]$ $-\frac{1}{4}e^{3} - e + \frac{3}{4}$
3 $[3, 3, -2w + 19]$ $-2$
5 $[5, 5, w]$ $\phantom{-}\frac{1}{4}e^{3} + e^{2} + e - \frac{3}{4}$
5 $[5, 5, w + 4]$ $-\frac{1}{4}e^{3} - e^{2} - e - \frac{9}{4}$
13 $[13, 13, w + 1]$ $\phantom{-}\frac{1}{12}e^{3} + \frac{1}{3}e^{2} - \frac{5}{3}e + \frac{3}{4}$
13 $[13, 13, w + 11]$ $\phantom{-}\frac{5}{12}e^{3} - \frac{1}{3}e^{2} + \frac{5}{3}e - \frac{5}{4}$
17 $[17, 17, w + 3]$ $\phantom{-}\frac{3}{4}e^{3} + e^{2} + 3e - \frac{9}{4}$
17 $[17, 17, w + 13]$ $-\frac{1}{4}e^{3} - e^{2} - 3e - \frac{9}{4}$
19 $[19, 19, w + 6]$ $-\frac{7}{12}e^{3} - \frac{1}{3}e^{2} - \frac{7}{3}e + \frac{7}{4}$
19 $[19, 19, w + 12]$ $\phantom{-}\frac{1}{12}e^{3} + \frac{1}{3}e^{2} + \frac{7}{3}e + \frac{3}{4}$
37 $[37, 37, w + 2]$ $-\frac{7}{12}e^{3} - \frac{7}{3}e^{2} - \frac{7}{3}e + \frac{7}{4}$
37 $[37, 37, w + 34]$ $\phantom{-}\frac{7}{12}e^{3} + \frac{7}{3}e^{2} + \frac{7}{3}e + \frac{21}{4}$
49 $[49, 7, -7]$ $-\frac{1}{2}e^{3} + \frac{19}{2}$
59 $[59, 59, -4w - 33]$ $-\frac{1}{2}e^{3} + \frac{15}{2}$
59 $[59, 59, 4w - 37]$ $-\frac{1}{2}e^{3} + \frac{15}{2}$
61 $[61, 61, w + 28]$ $-\frac{5}{12}e^{3} - \frac{5}{3}e^{2} + \frac{1}{3}e - \frac{15}{4}$
61 $[61, 61, w + 32]$ $-\frac{1}{12}e^{3} + \frac{5}{3}e^{2} - \frac{1}{3}e + \frac{1}{4}$
71 $[71, 71, w + 22]$ $-\frac{3}{4}e^{3} + e^{2} - 3e + \frac{9}{4}$
71 $[71, 71, w + 48]$ $-\frac{1}{4}e^{3} - e^{2} + 3e - \frac{9}{4}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).