Properties

 Label 4.4.11025.1-9.1-d Base field $$\Q(\sqrt{5}, \sqrt{21})$$ Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, -\frac{1}{8}w^{3} + \frac{17}{8}w + \frac{3}{2}]$ Dimension $4$ CM no Base change yes

Related objects

• L-function not available

Base field $$\Q(\sqrt{5}, \sqrt{21})$$

Generator $$w$$, with minimal polynomial $$x^{4} - 13x^{2} + 16$$; narrow class number $$2$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 3, -\frac{1}{8}w^{3} + \frac{17}{8}w + \frac{3}{2}]$ Dimension: $4$ CM: no Base change: yes Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 28x^{2} + 176$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{11}{4}w + 5]$ $-\frac{1}{2}e^{2} + 7$
4 $[4, 2, \frac{1}{8}w^{3} - \frac{1}{2}w^{2} - \frac{5}{8}w + \frac{3}{2}]$ $-\frac{1}{2}e^{2} + 7$
5 $[5, 5, -\frac{3}{8}w^{3} + \frac{35}{8}w - \frac{1}{2}]$ $\phantom{-}e$
5 $[5, 5, \frac{3}{8}w^{3} - \frac{35}{8}w - \frac{1}{2}]$ $-e$
9 $[9, 3, -\frac{1}{8}w^{3} + \frac{17}{8}w + \frac{3}{2}]$ $-1$
41 $[41, 41, \frac{1}{8}w^{3} - \frac{1}{8}w + \frac{3}{2}]$ $-\frac{1}{2}e^{3} + 7e$
41 $[41, 41, \frac{3}{8}w^{3} - \frac{35}{8}w + \frac{3}{2}]$ $\phantom{-}\frac{1}{2}e^{3} - 7e$
41 $[41, 41, \frac{3}{8}w^{3} - \frac{35}{8}w - \frac{3}{2}]$ $-\frac{1}{2}e^{3} + 7e$
41 $[41, 41, -\frac{1}{8}w^{3} + \frac{1}{8}w + \frac{3}{2}]$ $\phantom{-}\frac{1}{2}e^{3} - 7e$
49 $[49, 7, \frac{1}{8}w^{3} - \frac{17}{8}w + \frac{7}{2}]$ $\phantom{-}14$
59 $[59, 59, \frac{5}{8}w^{3} - \frac{53}{8}w - \frac{5}{2}]$ $\phantom{-}\frac{1}{2}e^{3} - 8e$
59 $[59, 59, -\frac{7}{8}w^{3} + \frac{3}{2}w^{2} + \frac{83}{8}w - \frac{35}{2}]$ $\phantom{-}\frac{1}{2}e^{3} - 8e$
59 $[59, 59, -\frac{3}{4}w^{3} + \frac{3}{2}w^{2} + \frac{33}{4}w - 16]$ $-\frac{1}{2}e^{3} + 8e$
59 $[59, 59, \frac{5}{8}w^{3} - \frac{53}{8}w + \frac{5}{2}]$ $-\frac{1}{2}e^{3} + 8e$
79 $[79, 79, \frac{3}{8}w^{3} - w^{2} - \frac{35}{8}w + \frac{21}{2}]$ $-2e^{2} + 32$
79 $[79, 79, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 5]$ $-2e^{2} + 32$
79 $[79, 79, \frac{7}{8}w^{3} - \frac{79}{8}w - \frac{1}{2}]$ $-2e^{2} + 32$
79 $[79, 79, -\frac{3}{8}w^{3} - w^{2} + \frac{35}{8}w + \frac{21}{2}]$ $-2e^{2} + 32$
89 $[89, 89, \frac{1}{8}w^{3} - \frac{1}{8}w - \frac{5}{2}]$ $-3e$
89 $[89, 89, \frac{3}{8}w^{3} - \frac{35}{8}w + \frac{5}{2}]$ $-3e$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9,3,-\frac{1}{8}w^{3}+\frac{17}{8}w+\frac{3}{2}]$ $1$