Properties

Label 4.4.11197.1-23.2-c
Base field 4.4.11197.1
Weight $[2, 2, 2, 2]$
Level norm $23$
Level $[23, 23, -w^{2} + 3]$
Dimension $12$
CM no
Base change no

Related objects

Downloads

Learn more

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 $[97, 97, w^{3} - w^{2} - 4w - 3]$ $\phantom{-}\frac{3}{16}e^{10} - \frac{55}{8}e^{8} + \frac{387}{4}e^{6} - \frac{1299}{2}e^{4} + \frac{4133}{2}e^{2} - 2475$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, -w^{2} + 3]$ $1$