# Properties

 Label 4.4.1125.1-121.1-a Base field $$\Q(\zeta_{15})^+$$ Weight $[2, 2, 2, 2]$ Level norm $121$ Level $[121, 11, -w^{3} + 3w + 3]$ Dimension $6$ CM no Base change yes

# Related objects

• L-function not available

## Base field $$\Q(\zeta_{15})^+$$

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[121, 11, -w^{3} + 3w + 3]$ Dimension: $6$ CM: no Base change: yes Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 24x^{4} + 112x^{2} - 64$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 1]$ $\phantom{-}e$
9 $[9, 3, w^{3} + w^{2} - 4w - 3]$ $-\frac{1}{16}e^{5} + \frac{5}{4}e^{3} - 3e$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{2}e^{2} - 1$
29 $[29, 29, -w^{3} - w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{8}e^{5} - 3e^{3} + 12e$
29 $[29, 29, -w^{2} + w + 3]$ $\phantom{-}\frac{1}{4}e^{3} - 4e$
29 $[29, 29, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}\frac{1}{8}e^{5} - 3e^{3} + 12e$
29 $[29, 29, 2w^{3} + w^{2} - 7w]$ $\phantom{-}\frac{1}{4}e^{3} - 4e$
31 $[31, 31, -2w + 1]$ $-\frac{1}{8}e^{4} + 2e^{2}$
31 $[31, 31, 2w^{2} - 5]$ $\phantom{-}\frac{1}{4}e^{4} - 5e^{2} + 10$
31 $[31, 31, 2w^{3} + 2w^{2} - 6w - 3]$ $\phantom{-}\frac{1}{4}e^{4} - 5e^{2} + 10$
31 $[31, 31, 2w^{3} - 8w + 1]$ $-\frac{1}{8}e^{4} + 2e^{2}$
59 $[59, 59, w^{3} + w^{2} - 2w - 5]$ $\phantom{-}\frac{1}{2}e^{3} - 8e$
59 $[59, 59, -w^{3} + 2w^{2} + 4w - 5]$ $-\frac{3}{16}e^{5} + 4e^{3} - 13e$
59 $[59, 59, -3w^{3} + 10w - 4]$ $\phantom{-}\frac{1}{2}e^{3} - 8e$
59 $[59, 59, -2w^{3} - w^{2} + 7w - 2]$ $-\frac{3}{16}e^{5} + 4e^{3} - 13e$
61 $[61, 61, 4w^{3} + w^{2} - 13w - 1]$ $-\frac{1}{4}e^{4} + 4e^{2} - 2$
61 $[61, 61, 2w^{3} - w^{2} - 5w + 2]$ $-\frac{1}{4}e^{4} + 4e^{2} - 2$
61 $[61, 61, -3w^{3} - w^{2} + 8w]$ $\phantom{-}\frac{1}{8}e^{4} - 3e^{2} + 8$
61 $[61, 61, 3w^{3} - w^{2} - 10w + 5]$ $\phantom{-}\frac{1}{8}e^{4} - 3e^{2} + 8$
89 $[89, 89, w^{3} + w^{2} - w - 4]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + 4e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$121$ $[121, 11, -w^{3} + 3w + 3]$ $1$