# Properties

 Label 4.4.17609.1-14.1-f Base field 4.4.17609.1 Weight $[2, 2, 2, 2]$ Level norm $14$ Level $[14, 14, -w^{3} - w^{2} + 6w]$ Dimension $7$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.17609.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 10x - 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[14, 14, -w^{3} - w^{2} + 6w]$ Dimension: $7$ CM: no Base change: no Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{7} - 6x^{6} - 5x^{5} + 79x^{4} - 91x^{3} - 82x^{2} + 76x - 8$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}1$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 6w - 2]$ $\phantom{-}1$
8 $[8, 2, w^{3} - 7w + 3]$ $-\frac{1}{24}e^{6} + \frac{7}{8}e^{4} + \frac{7}{24}e^{3} - \frac{115}{24}e^{2} - \frac{8}{3}e + \frac{23}{6}$
11 $[11, 11, -w^{3} + 6w - 4]$ $-\frac{1}{6}e^{5} + \frac{2}{3}e^{4} + \frac{11}{6}e^{3} - \frac{49}{6}e^{2} + \frac{3}{2}e + \frac{13}{3}$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $\phantom{-}\frac{1}{12}e^{6} - \frac{2}{3}e^{5} - \frac{1}{12}e^{4} + \frac{35}{4}e^{3} - \frac{133}{12}e^{2} - \frac{26}{3}e + \frac{17}{3}$
17 $[17, 17, -w^{2} - w + 3]$ $-\frac{1}{8}e^{6} + \frac{2}{3}e^{5} + \frac{23}{24}e^{4} - \frac{203}{24}e^{3} + \frac{175}{24}e^{2} + 5e - \frac{29}{6}$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $\phantom{-}\frac{13}{24}e^{6} - \frac{8}{3}e^{5} - \frac{113}{24}e^{4} + \frac{853}{24}e^{3} - \frac{187}{8}e^{2} - \frac{127}{3}e + \frac{29}{2}$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $-\frac{1}{12}e^{6} + \frac{2}{3}e^{5} + \frac{1}{12}e^{4} - \frac{39}{4}e^{3} + \frac{133}{12}e^{2} + \frac{59}{3}e - \frac{11}{3}$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}\frac{1}{12}e^{6} - \frac{1}{6}e^{5} - \frac{13}{12}e^{4} + \frac{5}{4}e^{3} + \frac{5}{12}e^{2} + \frac{53}{6}e + \frac{2}{3}$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $-\frac{1}{2}e^{6} + \frac{5}{2}e^{5} + \frac{9}{2}e^{4} - 34e^{3} + 20e^{2} + \frac{97}{2}e - 17$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $\phantom{-}\frac{1}{24}e^{6} - \frac{7}{8}e^{4} + \frac{17}{24}e^{3} + \frac{91}{24}e^{2} - \frac{22}{3}e + \frac{7}{6}$
59 $[59, 59, -2w^{3} + 13w - 6]$ $-\frac{1}{6}e^{6} + e^{5} + \frac{1}{2}e^{4} - \frac{77}{6}e^{3} + \frac{113}{6}e^{2} + \frac{34}{3}e - \frac{38}{3}$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $-2e + 4$
59 $[59, 59, w^{2} + w - 1]$ $-\frac{1}{6}e^{6} + e^{5} + \frac{3}{2}e^{4} - \frac{83}{6}e^{3} + \frac{35}{6}e^{2} + \frac{61}{3}e + \frac{4}{3}$
59 $[59, 59, w^{2} + 2w - 6]$ $\phantom{-}\frac{1}{8}e^{6} - \frac{1}{2}e^{5} - \frac{13}{8}e^{4} + \frac{53}{8}e^{3} + \frac{15}{8}e^{2} - \frac{17}{2}e - \frac{3}{2}$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{7}{6}e^{5} - \frac{31}{12}e^{4} + \frac{193}{12}e^{3} - \frac{89}{12}e^{2} - \frac{49}{2}e + \frac{40}{3}$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $\phantom{-}\frac{1}{6}e^{6} - \frac{5}{6}e^{5} - \frac{7}{6}e^{4} + 11e^{3} - \frac{32}{3}e^{2} - \frac{77}{6}e + \frac{37}{3}$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $\phantom{-}\frac{1}{8}e^{6} - \frac{1}{3}e^{5} - \frac{55}{24}e^{4} + \frac{115}{24}e^{3} + \frac{265}{24}e^{2} - 11e - \frac{59}{6}$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{12}e^{6} + \frac{1}{6}e^{5} - \frac{29}{12}e^{4} - \frac{29}{12}e^{3} + \frac{67}{4}e^{2} + \frac{23}{6}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 1]$ $-1$
$7$ $[7, 7, -w^{3} + 6w - 2]$ $-1$