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

Downloads

Learn more about

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:
\(x^{5} \) \(\mathstrut -\mathstrut 3x^{4} \) \(\mathstrut -\mathstrut 14x^{3} \) \(\mathstrut +\mathstrut 38x^{2} \) \(\mathstrut +\mathstrut 17x \) \(\mathstrut -\mathstrut 35\)

  Show full eigenvalues   Hide large eigenvalues

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