# Properties

 Label 6.6.300125.1-125.1-c Base field 6.6.300125.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $125$ Level $[125, 5, 4w^{5} - w^{4} - 29w^{3} - 13w^{2} + 19w + 2]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 6.6.300125.1

Generator $$w$$, with minimal polynomial $$x^{6} - x^{5} - 7x^{4} + 2x^{3} + 7x^{2} - 2x - 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[125, 5, 4w^{5} - w^{4} - 29w^{3} - 13w^{2} + 19w + 2]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 10x^{5} - 84x^{4} + 880x^{3} - 112x^{2} - 4224x + 1728$$
Norm Prime Eigenvalue
29 $[29, 29, -9w^{5} + 3w^{4} + 64w^{3} + 26w^{2} - 40w - 10]$ $-\frac{1}{1944}e^{5} + \frac{23}{1944}e^{4} + \frac{7}{486}e^{3} - \frac{277}{243}e^{2} + \frac{152}{81}e + \frac{88}{9}$
29 $[29, 29, w^{5} - 7w^{3} - 5w^{2} + 2w + 2]$ $\phantom{-}\frac{7}{1296}e^{5} - \frac{31}{648}e^{4} - \frac{157}{324}e^{3} + \frac{661}{162}e^{2} + \frac{53}{27}e - \frac{32}{3}$
29 $[29, 29, w^{4} - w^{3} - 6w^{2} + 2]$ $\phantom{-}e$
29 $[29, 29, 5w^{5} - w^{4} - 36w^{3} - 19w^{2} + 21w + 9]$ $-\frac{1}{1944}e^{5} - \frac{1}{486}e^{4} + \frac{95}{972}e^{3} + \frac{121}{486}e^{2} - \frac{388}{81}e - \frac{2}{9}$
29 $[29, 29, -w^{5} + w^{4} + 7w^{3} - 2w^{2} - 6w + 1]$ $-\frac{7}{3888}e^{5} + \frac{5}{243}e^{4} + \frac{65}{486}e^{3} - \frac{805}{486}e^{2} + \frac{100}{81}e + \frac{20}{9}$
29 $[29, 29, 2w^{5} - 15w^{3} - 10w^{2} + 11w + 5]$ $-\frac{5}{1944}e^{5} + \frac{17}{972}e^{4} + \frac{58}{243}e^{3} - \frac{745}{486}e^{2} - \frac{104}{81}e + \frac{80}{9}$
41 $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ $\phantom{-}\frac{1}{1296}e^{5} - \frac{5}{1296}e^{4} - \frac{17}{162}e^{3} + \frac{26}{81}e^{2} + \frac{77}{27}e + \frac{7}{3}$
41 $[41, 41, -5w^{5} + 2w^{4} + 36w^{3} + 11w^{2} - 25w - 2]$ $\phantom{-}\frac{1}{1296}e^{5} - \frac{7}{648}e^{4} - \frac{41}{648}e^{3} + \frac{329}{324}e^{2} - \frac{13}{27}e - \frac{8}{3}$
41 $[41, 41, 6w^{5} - w^{4} - 44w^{3} - 23w^{2} + 30w + 8]$ $\phantom{-}\frac{1}{972}e^{5} - \frac{19}{1944}e^{4} - \frac{109}{972}e^{3} + \frac{433}{486}e^{2} + \frac{391}{162}e - \frac{23}{9}$
41 $[41, 41, 13w^{5} - 4w^{4} - 93w^{3} - 39w^{2} + 59w + 16]$ $-\frac{1}{432}e^{5} + \frac{1}{54}e^{4} + \frac{25}{108}e^{3} - \frac{179}{108}e^{2} - \frac{23}{9}e + 11$
41 $[41, 41, -4w^{5} + 30w^{3} + 19w^{2} - 19w - 8]$ $-\frac{5}{2592}e^{5} + \frac{13}{648}e^{4} + \frac{29}{162}e^{3} - \frac{557}{324}e^{2} - \frac{35}{27}e + \frac{23}{3}$
41 $[41, 41, w^{5} - 7w^{3} - 6w^{2} + 2w + 3]$ $\phantom{-}\frac{13}{7776}e^{5} - \frac{55}{3888}e^{4} - \frac{253}{1944}e^{3} + \frac{1117}{972}e^{2} - \frac{151}{162}e + \frac{11}{9}$
49 $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ $\phantom{-}0$
64 $[64, 2, -2]$ $\phantom{-}4$
71 $[71, 71, -8w^{5} + w^{4} + 58w^{3} + 34w^{2} - 34w - 16]$ $\phantom{-}\frac{5}{1296}e^{5} - \frac{13}{324}e^{4} - \frac{29}{81}e^{3} + \frac{557}{162}e^{2} + \frac{167}{54}e - \frac{31}{3}$
71 $[71, 71, -6w^{5} + 2w^{4} + 42w^{3} + 18w^{2} - 23w - 6]$ $-\frac{7}{1944}e^{5} + \frac{53}{1944}e^{4} + \frac{601}{1944}e^{3} - \frac{2113}{972}e^{2} - \frac{43}{81}e + \frac{22}{9}$
71 $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 27w^{2} - 38w - 10]$ $-\frac{19}{7776}e^{5} + \frac{31}{972}e^{4} + \frac{47}{243}e^{3} - \frac{2779}{972}e^{2} + \frac{128}{81}e + \frac{103}{9}$
71 $[71, 71, 4w^{5} - 30w^{3} - 19w^{2} + 20w + 8]$ $\phantom{-}\frac{17}{3888}e^{5} - \frac{121}{3888}e^{4} - \frac{443}{972}e^{3} + \frac{667}{243}e^{2} + \frac{490}{81}e - \frac{109}{9}$
71 $[71, 71, -10w^{5} + 3w^{4} + 72w^{3} + 30w^{2} - 48w - 10]$ $\phantom{-}\frac{1}{864}e^{5} - \frac{7}{432}e^{4} - \frac{7}{216}e^{3} + \frac{151}{108}e^{2} - \frac{85}{18}e - 5$
71 $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 26w^{2} - 37w - 8]$ $-\frac{13}{3888}e^{5} + \frac{55}{1944}e^{4} + \frac{167}{486}e^{3} - \frac{2477}{972}e^{2} - \frac{443}{81}e + \frac{131}{9}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$125$ $[125, 5, 4w^{5} - w^{4} - 29w^{3} - 13w^{2} + 19w + 2]$ $1$