Base field 4.4.14272.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 36x^{10} + 492x^{8} - 3144x^{6} + 9168x^{4} - 9696x^{2} + 3136\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{3} + 3w^{2} + w - 2]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ | $\phantom{-}\frac{3}{64}e^{10} - \frac{43}{32}e^{8} + \frac{105}{8}e^{6} - \frac{389}{8}e^{4} + \frac{95}{2}e^{2} - \frac{15}{2}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $\phantom{-}\frac{3}{224}e^{11} - \frac{47}{112}e^{9} + \frac{33}{7}e^{7} - \frac{633}{28}e^{5} + \frac{296}{7}e^{3} - \frac{153}{7}e$ |
| 13 | $[13, 13, -w + 2]$ | $-\frac{3}{64}e^{10} + \frac{43}{32}e^{8} - \frac{105}{8}e^{6} + \frac{389}{8}e^{4} - \frac{97}{2}e^{2} + \frac{31}{2}$ |
| 17 | $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ | $\phantom{-}\frac{5}{896}e^{11} - \frac{69}{448}e^{9} + \frac{157}{112}e^{7} - \frac{467}{112}e^{5} - \frac{41}{28}e^{3} + \frac{263}{28}e$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{4}e^{6} - 5e^{4} + 26e^{2} - 18$ |
| 19 | $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}e$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $-\frac{3}{224}e^{11} + \frac{47}{112}e^{9} - \frac{33}{7}e^{7} + \frac{633}{28}e^{5} - \frac{296}{7}e^{3} + \frac{153}{7}e$ |
| 27 | $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ | $-\frac{3}{224}e^{11} + \frac{47}{112}e^{9} - \frac{33}{7}e^{7} + \frac{633}{28}e^{5} - \frac{296}{7}e^{3} + \frac{160}{7}e$ |
| 29 | $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ | $\phantom{-}\frac{3}{224}e^{11} - \frac{47}{112}e^{9} + \frac{33}{7}e^{7} - \frac{633}{28}e^{5} + \frac{303}{7}e^{3} - \frac{209}{7}e$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ | $-\frac{15}{448}e^{11} + \frac{207}{224}e^{9} - \frac{471}{56}e^{7} + \frac{1457}{56}e^{5} - \frac{87}{14}e^{3} - \frac{89}{14}e$ |
| 41 | $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ | $\phantom{-}\frac{29}{896}e^{11} - \frac{445}{448}e^{9} + \frac{1213}{112}e^{7} - \frac{5531}{112}e^{5} + \frac{2327}{28}e^{3} - \frac{961}{28}e$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ | $-\frac{1}{64}e^{10} + \frac{17}{32}e^{8} - \frac{55}{8}e^{6} + \frac{327}{8}e^{4} - \frac{203}{2}e^{2} + \frac{117}{2}$ |
| 59 | $[59, 59, w - 4]$ | $\phantom{-}\frac{1}{16}e^{10} - \frac{15}{8}e^{8} + \frac{79}{4}e^{6} - \frac{171}{2}e^{4} + 134e^{2} - 60$ |
| 67 | $[67, 67, 2w^{2} - 3w - 8]$ | $\phantom{-}\frac{7}{64}e^{10} - \frac{103}{32}e^{8} + \frac{261}{8}e^{6} - \frac{1033}{8}e^{4} + \frac{311}{2}e^{2} - \frac{99}{2}$ |
| 73 | $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ | $-\frac{1}{128}e^{11} + \frac{17}{64}e^{9} - \frac{53}{16}e^{7} + \frac{295}{16}e^{5} - \frac{175}{4}e^{3} + \frac{117}{4}e$ |
| 89 | $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ | $\phantom{-}\frac{5}{896}e^{11} - \frac{69}{448}e^{9} + \frac{157}{112}e^{7} - \frac{467}{112}e^{5} - \frac{69}{28}e^{3} + \frac{543}{28}e$ |
| 97 | $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ | $-\frac{1}{16}e^{10} + \frac{15}{8}e^{8} - \frac{39}{2}e^{6} + \frac{161}{2}e^{4} - 109e^{2} + 56$ |
| 97 | $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ | $-\frac{13}{896}e^{11} + \frac{157}{448}e^{9} - \frac{257}{112}e^{7} - \frac{85}{112}e^{5} + \frac{969}{28}e^{3} - \frac{583}{28}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{3} + 3w^{2} + w - 2]$ | $1$ |