Properties

Label 2.2.120.1-15.1-j
Base field \(\Q(\sqrt{30}) \)
Weight $[2, 2]$
Level norm $15$
Level $[15, 15, w]$
Dimension $8$
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: $[15, 15, w]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $44$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} + 25x^{6} + 98x^{4} + 20x^{2} + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-\frac{68}{39}e^{7} - \frac{1694}{39}e^{5} - 167e^{3} - \frac{749}{39}e$
3 $[3, 3, w]$ $-\frac{2}{13}e^{7} - \frac{151}{39}e^{5} - \frac{47}{3}e^{3} - \frac{185}{39}e$
5 $[5, 5, -w + 5]$ $-1$
7 $[7, 7, w + 3]$ $\phantom{-}e$
7 $[7, 7, w + 4]$ $-\frac{62}{13}e^{7} - \frac{1543}{13}e^{5} - 454e^{3} - \frac{577}{13}e$
13 $[13, 13, w + 2]$ $-\frac{75}{13}e^{7} - \frac{1868}{13}e^{5} - 552e^{3} - \frac{837}{13}e$
13 $[13, 13, w + 11]$ $\phantom{-}\frac{7}{13}e^{7} + \frac{174}{13}e^{5} + 51e^{3} + \frac{88}{13}e$
17 $[17, 17, w + 8]$ $\phantom{-}\frac{149}{39}e^{7} + \frac{3713}{39}e^{5} + 367e^{3} + \frac{1979}{39}e$
17 $[17, 17, w + 9]$ $-\frac{31}{39}e^{7} - \frac{778}{39}e^{5} - 80e^{3} - \frac{1036}{39}e$
19 $[19, 19, w + 7]$ $\phantom{-}\frac{27}{13}e^{6} + \frac{673}{13}e^{4} + 199e^{2} + \frac{254}{13}$
19 $[19, 19, -w + 7]$ $-\frac{34}{13}e^{6} - \frac{847}{13}e^{4} - 250e^{2} - \frac{316}{13}$
29 $[29, 29, -w - 1]$ $-\frac{131}{39}e^{6} - \frac{3260}{39}e^{4} - 320e^{2} - \frac{1307}{39}$
29 $[29, 29, w - 1]$ $-\frac{58}{39}e^{6} - \frac{1438}{39}e^{4} - 139e^{2} - \frac{484}{39}$
37 $[37, 37, w + 17]$ $-\frac{82}{13}e^{7} - \frac{2042}{13}e^{5} - 603e^{3} - \frac{912}{13}e$
37 $[37, 37, w + 20]$ $\phantom{-}\frac{20}{13}e^{7} + \frac{499}{13}e^{5} + 149e^{3} + \frac{348}{13}e$
71 $[71, 71, 2w - 7]$ $\phantom{-}\frac{53}{39}e^{6} + \frac{441}{13}e^{4} + \frac{392}{3}e^{2} + \frac{163}{39}$
71 $[71, 71, -2w - 7]$ $-\frac{179}{39}e^{6} - \frac{1485}{13}e^{4} - \frac{1310}{3}e^{2} - \frac{1864}{39}$
83 $[83, 83, w + 14]$ $-\frac{54}{13}e^{7} - \frac{4025}{39}e^{5} - \frac{1174}{3}e^{3} - \frac{952}{39}e$
83 $[83, 83, w + 69]$ $-\frac{54}{13}e^{7} - \frac{4025}{39}e^{5} - \frac{1174}{3}e^{3} - \frac{952}{39}e$
101 $[101, 101, -7w + 37]$ $\phantom{-}\frac{142}{39}e^{6} + \frac{3539}{39}e^{4} + \frac{1049}{3}e^{2} + \frac{405}{13}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $\frac{2}{13}e^{7} + \frac{151}{39}e^{5} + \frac{47}{3}e^{3} + \frac{185}{39}e$
$5$ $[5, 5, -w + 5]$ $1$