Properties

Label 2.2.321.1-5.2-m
Base field \(\Q(\sqrt{321}) \)
Weight $[2, 2]$
Level norm $5$
Level $[5,5,-w + 1]$
Dimension $20$
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: $[5,5,-w + 1]$
Dimension: $20$
CM: no
Base change: no
Newspace dimension: $168$

Hecke eigenvalues ($q$-expansion)

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

\(x^{20} - x^{19} - 28x^{18} + 24x^{17} + 327x^{16} - 237x^{15} - 2064x^{14} + 1261x^{13} + 7642x^{12} - 3999x^{11} - 16920x^{10} + 7874x^{9} + 21988x^{8} - 9483x^{7} - 15757x^{6} + 6404x^{5} + 5386x^{4} - 1955x^{3} - 569x^{2} + 116x - 3\)

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5,5,-w + 1]$ $1$