# Properties

 Base field 4.4.2624.1 Weight [2, 2, 2, 2] Level norm 49 Level $[49, 7, w^{2} - 4w - 1]$ Label 4.4.2624.1-49.2-c Dimension 5 CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.2624.1

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

## Form

 Weight [2, 2, 2, 2] Level $[49, 7, w^{2} - 4w - 1]$ Label 4.4.2624.1-49.2-c Dimension 5 Is CM no Is base change yes Parent newspace dimension 7

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{5}$$ $$\mathstrut -\mathstrut 3x^{4}$$ $$\mathstrut -\mathstrut 14x^{3}$$ $$\mathstrut +\mathstrut 38x^{2}$$ $$\mathstrut +\mathstrut 17x$$ $$\mathstrut -\mathstrut 35$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 3w^{2} + w - 3]$ $\phantom{-}\frac{1}{11}e^{4} - \frac{5}{22}e^{3} - \frac{25}{22}e^{2} + \frac{47}{22}e + \frac{41}{22}$
7 $[7, 7, -w^{2} + w + 2]$ $\phantom{-}\frac{1}{11}e^{4} - \frac{5}{22}e^{3} - \frac{25}{22}e^{2} + \frac{47}{22}e + \frac{41}{22}$
17 $[17, 17, -w^{3} + 3w^{2} - 3]$ $-\frac{1}{11}e^{4} - \frac{3}{11}e^{3} + \frac{18}{11}e^{2} + \frac{37}{11}e - \frac{37}{11}$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $-\frac{1}{11}e^{4} - \frac{3}{11}e^{3} + \frac{18}{11}e^{2} + \frac{37}{11}e - \frac{37}{11}$
25 $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ $-\frac{1}{22}e^{4} + \frac{4}{11}e^{3} - \frac{2}{11}e^{2} - \frac{42}{11}e + \frac{117}{22}$
25 $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ $-\frac{1}{22}e^{4} + \frac{4}{11}e^{3} - \frac{2}{11}e^{2} - \frac{42}{11}e + \frac{117}{22}$
41 $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}\frac{5}{11}e^{4} - \frac{7}{11}e^{3} - \frac{79}{11}e^{2} + \frac{57}{11}e + \frac{152}{11}$
47 $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ $\phantom{-}\frac{3}{11}e^{4} - \frac{2}{11}e^{3} - \frac{43}{11}e^{2} + \frac{21}{11}e + \frac{23}{11}$
47 $[47, 47, 2w^{3} - 4w^{2} - 5w]$ $\phantom{-}\frac{3}{11}e^{4} - \frac{2}{11}e^{3} - \frac{43}{11}e^{2} + \frac{21}{11}e + \frac{23}{11}$
49 $[49, 7, w^{2} - 4w - 1]$ $-1$
71 $[71, 71, 2w - 3]$ $-\frac{5}{11}e^{4} + \frac{7}{11}e^{3} + \frac{57}{11}e^{2} - \frac{57}{11}e + \frac{2}{11}$
71 $[71, 71, -w^{3} + w^{2} + 6w - 2]$ $-\frac{5}{11}e^{4} + \frac{7}{11}e^{3} + \frac{57}{11}e^{2} - \frac{57}{11}e + \frac{2}{11}$
73 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ $-\frac{4}{11}e^{4} + \frac{10}{11}e^{3} + \frac{61}{11}e^{2} - \frac{138}{11}e - \frac{71}{11}$
73 $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ $-\frac{4}{11}e^{4} + \frac{10}{11}e^{3} + \frac{61}{11}e^{2} - \frac{138}{11}e - \frac{71}{11}$
73 $[73, 73, -w^{3} + 3w^{2} - 5]$ $\phantom{-}\frac{3}{22}e^{4} + \frac{9}{22}e^{3} - \frac{43}{22}e^{2} - \frac{155}{22}e + \frac{39}{11}$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}\frac{3}{22}e^{4} + \frac{9}{22}e^{3} - \frac{43}{22}e^{2} - \frac{155}{22}e + \frac{39}{11}$
79 $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ $-\frac{9}{22}e^{4} + \frac{3}{11}e^{3} + \frac{81}{11}e^{2} - \frac{15}{11}e - \frac{465}{22}$
79 $[79, 79, 2w^{3} - 3w^{2} - 5w]$ $-\frac{9}{22}e^{4} + \frac{3}{11}e^{3} + \frac{81}{11}e^{2} - \frac{15}{11}e - \frac{465}{22}$
81 $[81, 3, -3]$ $-\frac{6}{11}e^{4} + \frac{15}{11}e^{3} + \frac{86}{11}e^{2} - \frac{141}{11}e - \frac{68}{11}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
49 $[49, 7, w^{2} - 4w - 1]$ $1$