# Properties

 Label 4.4.6125.1-55.1-d Base field 4.4.6125.1 Weight $[2, 2, 2, 2]$ Level norm $55$ Level $[55, 55, -w^{3} - 2w^{2} + 5w + 11]$ Dimension $5$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.6125.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 9x^{2} + 9x + 11$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[55, 55, -w^{3} - 2w^{2} + 5w + 11]$ Dimension: $5$ 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:

 $$x^{5} + 3x^{4} - 39x^{3} - 119x^{2} + 322x + 920$$
Norm Prime Eigenvalue
5 $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ $-1$
11 $[11, 11, 2w^{3} + 3w^{2} - 12w - 11]$ $\phantom{-}1$
11 $[11, 11, -w^{3} - 2w^{2} + 6w + 9]$ $\phantom{-}e$
11 $[11, 11, w^{3} + w^{2} - 7w - 4]$ $-\frac{3}{8}e^{4} + \frac{1}{2}e^{3} + \frac{97}{8}e^{2} - \frac{33}{4}e - 79$
11 $[11, 11, w - 1]$ $\phantom{-}\frac{5}{16}e^{4} - \frac{1}{2}e^{3} - \frac{155}{16}e^{2} + \frac{67}{8}e + \frac{117}{2}$
16 $[16, 2, 2]$ $\phantom{-}\frac{7}{16}e^{4} - \frac{3}{4}e^{3} - \frac{221}{16}e^{2} + \frac{101}{8}e + \frac{169}{2}$
19 $[19, 19, -w^{2} + 4]$ $-\frac{7}{16}e^{4} + \frac{3}{4}e^{3} + \frac{221}{16}e^{2} - \frac{101}{8}e - \frac{175}{2}$
19 $[19, 19, 2w^{3} + 2w^{2} - 13w - 6]$ $-\frac{1}{16}e^{4} + \frac{1}{4}e^{3} + \frac{27}{16}e^{2} - \frac{43}{8}e - \frac{21}{2}$
19 $[19, 19, 3w^{3} + 4w^{2} - 18w - 16]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{1}{4}e^{3} - \frac{33}{8}e^{2} + \frac{17}{4}e + 27$
19 $[19, 19, -w^{3} - w^{2} + 5w + 3]$ $\phantom{-}\frac{3}{16}e^{4} - \frac{1}{4}e^{3} - \frac{105}{16}e^{2} + \frac{33}{8}e + \frac{91}{2}$
49 $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ $-\frac{3}{4}e^{4} + \frac{5}{4}e^{3} + \frac{49}{2}e^{2} - 22e - 166$
59 $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ $-e^{4} + \frac{5}{4}e^{3} + \frac{129}{4}e^{2} - \frac{41}{2}e - 208$
59 $[59, 59, 3w^{3} + 4w^{2} - 18w - 17]$ $\phantom{-}\frac{9}{16}e^{4} - \frac{3}{4}e^{3} - \frac{283}{16}e^{2} + \frac{99}{8}e + \frac{217}{2}$
59 $[59, 59, 2w^{3} + 3w^{2} - 11w - 13]$ $\phantom{-}\frac{11}{16}e^{4} - \frac{5}{4}e^{3} - \frac{353}{16}e^{2} + \frac{177}{8}e + \frac{283}{2}$
59 $[59, 59, -w^{3} - 2w^{2} + 7w + 9]$ $-\frac{7}{16}e^{4} + \frac{3}{4}e^{3} + \frac{221}{16}e^{2} - \frac{109}{8}e - \frac{179}{2}$
71 $[71, 71, 3w^{3} + 3w^{2} - 17w - 10]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{13}{2}e - 6$
71 $[71, 71, -2w^{3} - w^{2} + 14w + 2]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{1}{4}e^{3} - \frac{41}{8}e^{2} + \frac{21}{4}e + 43$
71 $[71, 71, 5w^{3} + 7w^{2} - 30w - 25]$ $-\frac{7}{16}e^{4} + \frac{3}{4}e^{3} + \frac{237}{16}e^{2} - \frac{109}{8}e - \frac{203}{2}$
71 $[71, 71, -3w^{3} - 4w^{2} + 16w + 16]$ $-\frac{5}{16}e^{4} + \frac{3}{4}e^{3} + \frac{159}{16}e^{2} - \frac{111}{8}e - \frac{129}{2}$
81 $[81, 3, -3]$ $-\frac{1}{4}e^{4} + \frac{1}{4}e^{3} + 8e^{2} - 5e - 54$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ $1$
$11$ $[11, 11, 2w^{3} + 3w^{2} - 12w - 11]$ $-1$