Properties

Base field \(\Q(\sqrt{55}) \)
Weight [2, 2]
Level norm 6
Level $[6,6,w - 7]$
Label 2.2.220.1-6.2-e
Dimension 8
CM no
Base change no

Related objects

Downloads

Learn more about

Base field \(\Q(\sqrt{55}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 55\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[6,6,w - 7]$
Label 2.2.220.1-6.2-e
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 32

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut +\mathstrut 18x^{6} \) \(\mathstrut +\mathstrut 81x^{4} \) \(\mathstrut +\mathstrut 53x^{2} \) \(\mathstrut +\mathstrut 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $-\frac{5}{106}e^{7} - \frac{47}{53}e^{5} - \frac{459}{106}e^{3} - \frac{399}{106}e$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{5}{106}e^{7} + \frac{47}{53}e^{5} + \frac{459}{106}e^{3} + \frac{399}{106}e$
5 $[5, 5, -2w + 15]$ $-\frac{7}{53}e^{6} - \frac{121}{53}e^{4} - \frac{473}{53}e^{2} - \frac{71}{53}$
11 $[11, 11, 3w - 22]$ $-\frac{10}{53}e^{6} - \frac{188}{53}e^{4} - \frac{865}{53}e^{2} - \frac{321}{53}$
13 $[13, 13, w + 4]$ $\phantom{-}\frac{12}{53}e^{7} + \frac{215}{53}e^{5} + \frac{932}{53}e^{3} + \frac{417}{53}e$
13 $[13, 13, w + 9]$ $-\frac{67}{106}e^{7} - \frac{598}{53}e^{5} - \frac{5239}{106}e^{3} - \frac{2739}{106}e$
17 $[17, 17, w + 2]$ $\phantom{-}\frac{12}{53}e^{7} + \frac{215}{53}e^{5} + \frac{932}{53}e^{3} + \frac{258}{53}e$
17 $[17, 17, w + 15]$ $-\frac{29}{106}e^{7} - \frac{262}{53}e^{5} - \frac{2429}{106}e^{3} - \frac{2081}{106}e$
19 $[19, 19, -w - 6]$ $\phantom{-}\frac{2}{53}e^{6} + \frac{27}{53}e^{4} + \frac{67}{53}e^{2} - \frac{63}{53}$
19 $[19, 19, w - 6]$ $-\frac{2}{53}e^{6} - \frac{27}{53}e^{4} - \frac{14}{53}e^{2} + \frac{116}{53}$
23 $[23, 23, w + 3]$ $\phantom{-}\frac{5}{53}e^{7} + \frac{94}{53}e^{5} + \frac{512}{53}e^{3} + \frac{876}{53}e$
23 $[23, 23, w + 20]$ $\phantom{-}\frac{19}{53}e^{7} + \frac{336}{53}e^{5} + \frac{1458}{53}e^{3} + \frac{859}{53}e$
47 $[47, 47, w + 14]$ $\phantom{-}\frac{60}{53}e^{7} + \frac{1075}{53}e^{5} + \frac{4713}{53}e^{3} + \frac{2297}{53}e$
47 $[47, 47, w + 33]$ $\phantom{-}\frac{77}{106}e^{7} + \frac{692}{53}e^{5} + \frac{6157}{106}e^{3} + \frac{3113}{106}e$
49 $[49, 7, -7]$ $\phantom{-}\frac{14}{53}e^{6} + \frac{242}{53}e^{4} + \frac{999}{53}e^{2} + \frac{301}{53}$
67 $[67, 67, w + 16]$ $-\frac{99}{106}e^{7} - \frac{867}{53}e^{5} - \frac{7371}{106}e^{3} - \frac{3533}{106}e$
67 $[67, 67, w + 51]$ $-\frac{44}{53}e^{7} - \frac{806}{53}e^{5} - \frac{3753}{53}e^{3} - \frac{2642}{53}e$
73 $[73, 73, w + 36]$ $\phantom{-}\frac{1}{106}e^{7} + \frac{20}{53}e^{5} + \frac{431}{106}e^{3} + \frac{1373}{106}e$
73 $[73, 73, w + 37]$ $\phantom{-}\frac{70}{53}e^{7} + \frac{1263}{53}e^{5} + \frac{5684}{53}e^{3} + \frac{3519}{53}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,-w + 1]$ $\frac{5}{106}e^{7} + \frac{47}{53}e^{5} + \frac{459}{106}e^{3} + \frac{399}{106}e$
3 $[3,3,-w + 1]$ $-\frac{5}{106}e^{7} - \frac{47}{53}e^{5} - \frac{459}{106}e^{3} - \frac{399}{106}e$