# Properties

 Label 6.6.1683101.1-1.1-a Base field 6.6.1683101.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $1$ Level $[1, 1, 1]$ Dimension $4$ CM no Base change yes

# Related objects

• L-function not available

## Base field 6.6.1683101.1

Generator $$w$$, with minimal polynomial $$x^{6} - 3x^{5} - 4x^{4} + 13x^{3} + 7x^{2} - 14x - 7$$; narrow class number $$1$$ and class number $$1$$.

## Form

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

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 2x^{3} - 19x^{2} + 24x + 12$$
Norm Prime Eigenvalue
7 $[7, 7, w]$ $\phantom{-}e$
7 $[7, 7, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + 5]$ $\phantom{-}e$
13 $[13, 13, w^{2} - 3]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - \frac{17}{4}e + \frac{7}{2}$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - \frac{17}{4}e + \frac{7}{2}$
29 $[29, 29, w^{4} - 2w^{3} - 4w^{2} + 4w + 6]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{23}{4}e - \frac{1}{2}$
29 $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 6w - 5]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{23}{4}e - \frac{1}{2}$
41 $[41, 41, -w^{2} + 4]$ $-\frac{1}{4}e^{3} - \frac{1}{2}e^{2} + \frac{21}{4}e + \frac{11}{2}$
41 $[41, 41, -w^{2} + 2w + 3]$ $-\frac{1}{4}e^{3} - \frac{1}{2}e^{2} + \frac{21}{4}e + \frac{11}{2}$
43 $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 8e - 2$
43 $[43, 43, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 8e - 2$
64 $[64, 2, -2]$ $-\frac{1}{2}e^{2} - \frac{5}{2}e + 14$
71 $[71, 71, w^{5} - 3w^{4} - w^{3} + 6w^{2} - 2w + 2]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 5$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} - w + 5]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 5$
71 $[71, 71, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 5$
71 $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 19w^{2} - w - 12]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 5$
83 $[83, 83, -w^{4} + w^{3} + 5w^{2} - w - 6]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{17}{2}e - 1$
83 $[83, 83, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{17}{2}e - 1$
97 $[97, 97, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ $-\frac{1}{4}e^{3} + e^{2} + \frac{7}{4}e - \frac{13}{2}$
97 $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + 2w - 2]$ $-\frac{1}{4}e^{3} + e^{2} + \frac{7}{4}e - \frac{13}{2}$
113 $[113, 113, -2w^{4} + 3w^{3} + 8w^{2} - 6w - 6]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - \frac{13}{4}e - \frac{15}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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