Properties

Base field 4.4.17725.1
Weight [2, 2, 2, 2]
Level norm 16
Level $[16, 2, 2]$
Label 4.4.17725.1-16.1-f
Dimension 6
CM no
Base change no

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Base field 4.4.17725.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[16, 2, 2]$
Label 4.4.17725.1-16.1-f
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 30

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut +\mathstrut 6x^{5} \) \(\mathstrut -\mathstrut 15x^{4} \) \(\mathstrut -\mathstrut 100x^{3} \) \(\mathstrut +\mathstrut 128x^{2} \) \(\mathstrut +\mathstrut 472x \) \(\mathstrut -\mathstrut 667\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}e$
9 $[9, 3, -w^{3} + 8w + 8]$ $-e - 2$
16 $[16, 2, 2]$ $\phantom{-}1$
19 $[19, 19, w + 1]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{5}{7}e^{4} - \frac{6}{7}e^{3} - \frac{38}{7}e^{2} + \frac{5}{7}e + \frac{40}{7}$
19 $[19, 19, -w^{2} + 6]$ $-\frac{1}{7}e^{5} - \frac{5}{7}e^{4} + \frac{13}{7}e^{3} + \frac{59}{7}e^{2} - \frac{61}{7}e - \frac{124}{7}$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{5}{7}e^{4} - \frac{13}{7}e^{3} - \frac{59}{7}e^{2} + \frac{61}{7}e + \frac{82}{7}$
19 $[19, 19, -w + 2]$ $-\frac{1}{7}e^{5} - \frac{5}{7}e^{4} + \frac{6}{7}e^{3} + \frac{38}{7}e^{2} - \frac{5}{7}e - \frac{26}{7}$
25 $[25, 5, 2w^{2} - 2w - 13]$ $-e^{2} - 2e + 6$
29 $[29, 29, -w^{2} + 9]$ $-\frac{1}{7}e^{5} - \frac{12}{7}e^{4} - \frac{22}{7}e^{3} + \frac{143}{7}e^{2} + \frac{254}{7}e - \frac{642}{7}$
29 $[29, 29, -w^{2} + 2w + 6]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{12}{7}e^{4} + \frac{15}{7}e^{3} - \frac{157}{7}e^{2} - \frac{198}{7}e + \frac{635}{7}$
29 $[29, 29, w^{2} - 7]$ $-\frac{1}{7}e^{5} + \frac{2}{7}e^{4} + \frac{41}{7}e^{3} - \frac{39}{7}e^{2} - \frac{306}{7}e + \frac{443}{7}$
29 $[29, 29, -w^{2} + 2w + 8]$ $\phantom{-}\frac{1}{7}e^{5} - \frac{2}{7}e^{4} - \frac{34}{7}e^{3} + \frac{67}{7}e^{2} + \frac{278}{7}e - \frac{562}{7}$
31 $[31, 31, -2w^{2} + w + 12]$ $-\frac{2}{7}e^{5} - \frac{10}{7}e^{4} + \frac{19}{7}e^{3} + \frac{104}{7}e^{2} - \frac{59}{7}e - \frac{206}{7}$
31 $[31, 31, 2w^{2} - 3w - 11]$ $\phantom{-}\frac{2}{7}e^{5} + \frac{10}{7}e^{4} - \frac{19}{7}e^{3} - \frac{90}{7}e^{2} + \frac{87}{7}e + \frac{80}{7}$
41 $[41, 41, -w]$ $\phantom{-}\frac{1}{7}e^{5} - \frac{2}{7}e^{4} - \frac{34}{7}e^{3} + \frac{60}{7}e^{2} + \frac{257}{7}e - \frac{492}{7}$
41 $[41, 41, -w + 1]$ $-\frac{1}{7}e^{5} - \frac{12}{7}e^{4} - \frac{22}{7}e^{3} + \frac{136}{7}e^{2} + \frac{247}{7}e - \frac{558}{7}$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $-\frac{1}{7}e^{5} + \frac{2}{7}e^{4} + \frac{34}{7}e^{3} - \frac{60}{7}e^{2} - \frac{264}{7}e + \frac{478}{7}$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{12}{7}e^{4} + \frac{22}{7}e^{3} - \frac{136}{7}e^{2} - \frac{240}{7}e + \frac{558}{7}$
61 $[61, 61, 2w^{2} - 3w - 14]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{12}{7}e^{4} + \frac{22}{7}e^{3} - \frac{157}{7}e^{2} - \frac{275}{7}e + \frac{789}{7}$
61 $[61, 61, 2w^{2} - w - 15]$ $-\frac{1}{7}e^{5} + \frac{2}{7}e^{4} + \frac{34}{7}e^{3} - \frac{81}{7}e^{2} - \frac{313}{7}e + \frac{695}{7}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
16 $[16, 2, 2]$ $-1$