# Properties

 Label 4.4.5125.1-49.2-a Base field 4.4.5125.1 Weight $[2, 2, 2, 2]$ Level norm $49$ Level $[49,7,-2w^{2} + w + 9]$ Dimension $7$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.5125.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 6x^{2} + 7x + 11$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[49,7,-2w^{2} + w + 9]$ Dimension: $7$ CM: no Base change: no Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{7} + 3x^{6} - 8x^{5} - 21x^{4} + 19x^{3} + 31x^{2} - 5$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 2w + 3]$ $\phantom{-}e$
9 $[9, 3, w^{3} - 3w^{2} - 2w + 9]$ $-\frac{1}{2}e^{6} - \frac{3}{2}e^{5} + \frac{7}{2}e^{4} + 9e^{3} - 7e^{2} - \frac{17}{2}e$
9 $[9, 3, -w^{3} + 5w + 5]$ $-e^{6} - \frac{5}{2}e^{5} + \frac{19}{2}e^{4} + \frac{31}{2}e^{3} - 29e^{2} - 10e + \frac{15}{2}$
11 $[11, 11, w]$ $\phantom{-}\frac{1}{2}e^{5} + \frac{5}{2}e^{4} - \frac{3}{2}e^{3} - 13e^{2} + 3e + \frac{11}{2}$
11 $[11, 11, w - 1]$ $-\frac{1}{2}e^{5} - \frac{3}{2}e^{4} + \frac{7}{2}e^{3} + 8e^{2} - 8e - \frac{9}{2}$
16 $[16, 2, 2]$ $-\frac{3}{2}e^{6} - 4e^{5} + 13e^{4} + \frac{47}{2}e^{3} - 39e^{2} - \frac{31}{2}e + \frac{21}{2}$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{5}{2}e^{6} + 6e^{5} - 23e^{4} - \frac{75}{2}e^{3} + 66e^{2} + \frac{67}{2}e - \frac{25}{2}$
19 $[19, 19, w^{3} - w^{2} - 4w + 2]$ $-\frac{1}{2}e^{6} - e^{5} + 6e^{4} + \frac{17}{2}e^{3} - 20e^{2} - \frac{21}{2}e + \frac{15}{2}$
29 $[29, 29, w^{3} - 4w^{2} - w + 10]$ $-e^{6} - \frac{3}{2}e^{5} + \frac{25}{2}e^{4} + \frac{23}{2}e^{3} - 43e^{2} - 11e + \frac{35}{2}$
29 $[29, 29, -w^{3} + 3w^{2} + w - 7]$ $\phantom{-}\frac{1}{2}e^{6} + \frac{1}{2}e^{5} - \frac{13}{2}e^{4} - 5e^{3} + 19e^{2} + \frac{13}{2}e$
41 $[41, 41, 3w^{2} - 2w - 10]$ $-\frac{5}{2}e^{6} - 6e^{5} + 23e^{4} + \frac{73}{2}e^{3} - 67e^{2} - \frac{55}{2}e + \frac{31}{2}$
49 $[49, 7, -2w^{2} + 3w + 8]$ $-\frac{3}{2}e^{6} - 3e^{5} + 15e^{4} + \frac{35}{2}e^{3} - 48e^{2} - \frac{25}{2}e + \frac{45}{2}$
49 $[49, 7, w^{3} - 2w^{2} - 2w + 5]$ $-1$
71 $[71, 71, -w - 3]$ $\phantom{-}\frac{1}{2}e^{6} + e^{5} - 7e^{4} - \frac{19}{2}e^{3} + 26e^{2} + \frac{23}{2}e - \frac{21}{2}$
71 $[71, 71, w - 4]$ $\phantom{-}3e^{6} + \frac{13}{2}e^{5} - \frac{57}{2}e^{4} - \frac{75}{2}e^{3} + 87e^{2} + 22e - \frac{61}{2}$
79 $[79, 79, -w^{3} + w^{2} + 3w + 3]$ $\phantom{-}\frac{3}{2}e^{6} + \frac{7}{2}e^{5} - \frac{31}{2}e^{4} - 24e^{3} + 47e^{2} + \frac{45}{2}e$
79 $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}\frac{1}{2}e^{6} + \frac{1}{2}e^{5} - \frac{9}{2}e^{4} - e^{3} + 10e^{2} - \frac{11}{2}e$
89 $[89, 89, w^{3} - 3w^{2} - 3w + 7]$ $-2e^{6} - 6e^{5} + 16e^{4} + 35e^{3} - 47e^{2} - 21e + 15$
89 $[89, 89, w^{3} - 6w - 2]$ $-\frac{1}{2}e^{6} - \frac{1}{2}e^{5} + \frac{15}{2}e^{4} + 7e^{3} - 25e^{2} - \frac{27}{2}e + 5$
101 $[101, 101, 2w^{3} - 5w^{2} - 3w + 9]$ $-\frac{1}{2}e^{5} - \frac{7}{2}e^{4} + \frac{1}{2}e^{3} + 20e^{2} - \frac{19}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$49$ $[49,7,-2w^{2} + w + 9]$ $1$