Base field 4.4.11197.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[23, 23, -w^{2} + 3]$ |
Dimension: | $12$ |
CM: | no |
Base change: | no |
Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} - 42x^{10} + 708x^{8} - 6120x^{6} + 28584x^{4} - 68400x^{2} + 65536\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ | $-\frac{29}{1024}e^{11} + \frac{545}{512}e^{9} - \frac{3917}{256}e^{7} + \frac{13353}{128}e^{5} - \frac{42817}{128}e^{3} + \frac{25671}{64}e$ |
11 | $[11, 11, -w - 2]$ | $\phantom{-}\frac{1}{16}e^{10} - \frac{19}{8}e^{8} + \frac{69}{2}e^{6} - 238e^{4} + \frac{1551}{2}e^{2} - 951$ |
11 | $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{1}{2}e^{3} + 4e$ |
13 | $[13, 13, -w^{2} + 2w + 2]$ | $-\frac{53}{1024}e^{11} + \frac{985}{512}e^{9} - \frac{7013}{256}e^{7} + \frac{23777}{128}e^{5} - \frac{76345}{128}e^{3} + \frac{46223}{64}e$ |
16 | $[16, 2, 2]$ | $-\frac{1}{4}e^{6} + \frac{11}{2}e^{4} - 37e^{2} + 77$ |
19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ | $-\frac{23}{1024}e^{11} + \frac{419}{512}e^{9} - \frac{2919}{256}e^{7} + \frac{9659}{128}e^{5} - \frac{30211}{128}e^{3} + \frac{17941}{64}e$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $\phantom{-}\frac{11}{512}e^{11} - \frac{199}{256}e^{9} + \frac{1371}{128}e^{7} - \frac{4447}{64}e^{5} + \frac{13383}{64}e^{3} - \frac{7377}{32}e$ |
23 | $[23, 23, -w^{2} + 3]$ | $-1$ |
27 | $[27, 3, w^{3} - 3w^{2} - w + 4]$ | $-\frac{5}{512}e^{11} + \frac{105}{256}e^{9} - \frac{853}{128}e^{7} + \frac{3313}{64}e^{5} - \frac{12137}{64}e^{3} + \frac{8287}{32}e$ |
29 | $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ | $-\frac{9}{256}e^{11} + \frac{173}{128}e^{9} - \frac{1273}{64}e^{7} + \frac{4453}{32}e^{5} - \frac{14733}{32}e^{3} + \frac{9227}{16}e$ |
29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $-\frac{27}{1024}e^{11} + \frac{503}{512}e^{9} - \frac{3563}{256}e^{7} + \frac{11887}{128}e^{5} - \frac{37015}{128}e^{3} + \frac{21473}{64}e$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ | $-\frac{1}{4}e^{8} + \frac{15}{2}e^{6} - \frac{159}{2}e^{4} + 349e^{2} - 530$ |
47 | $[47, 47, w^{2} - 3w - 2]$ | $-\frac{37}{512}e^{11} + \frac{681}{256}e^{9} - \frac{4789}{128}e^{7} + \frac{15985}{64}e^{5} - \frac{50377}{64}e^{3} + \frac{29919}{32}e$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}\frac{3}{16}e^{10} - \frac{55}{8}e^{8} + \frac{387}{4}e^{6} - 651e^{4} + \frac{4177}{2}e^{2} - 2547$ |
67 | $[67, 67, -w^{3} + w^{2} + 5w - 1]$ | $\phantom{-}\frac{1}{16}e^{10} - \frac{19}{8}e^{8} + \frac{69}{2}e^{6} - \frac{473}{2}e^{4} + \frac{1505}{2}e^{2} - 877$ |
67 | $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ | $\phantom{-}\frac{1}{8}e^{10} - \frac{19}{4}e^{8} + \frac{275}{4}e^{6} - \frac{939}{2}e^{4} + 1500e^{2} - 1788$ |
83 | $[83, 83, -2w + 3]$ | $-\frac{1}{2}e^{6} + \frac{23}{2}e^{4} - 80e^{2} + 164$ |
89 | $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ | $\phantom{-}\frac{49}{1024}e^{11} - \frac{901}{512}e^{9} + \frac{6369}{256}e^{7} - \frac{21549}{128}e^{5} + \frac{69605}{128}e^{3} - \frac{43011}{64}e$ |
97 | $[97, 97, w^{3} - w^{2} - 4w - 3]$ | $\phantom{-}\frac{3}{16}e^{10} - \frac{55}{8}e^{8} + \frac{387}{4}e^{6} - \frac{1299}{2}e^{4} + \frac{4133}{2}e^{2} - 2475$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23, 23, -w^{2} + 3]$ | $1$ |