Base field 4.4.8957.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[23, 23, -w^{2} + 2]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} - 2x^{10} - 17x^{9} + 32x^{8} + 96x^{7} - 166x^{6} - 224x^{5} + 310x^{4} + 255x^{3} - 168x^{2} - 143x - 22\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + w^{2} + 5w]$ | $-\frac{1}{4}e^{7} + \frac{15}{4}e^{5} + \frac{1}{2}e^{4} - \frac{63}{4}e^{3} - 3e^{2} + \frac{73}{4}e + \frac{13}{2}$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $\phantom{-}\frac{1}{8}e^{10} - \frac{1}{8}e^{9} - 2e^{8} + \frac{7}{4}e^{7} + \frac{19}{2}e^{6} - \frac{15}{2}e^{5} - \frac{51}{4}e^{4} + \frac{33}{4}e^{3} - \frac{21}{8}e^{2} + \frac{13}{8}e + \frac{23}{4}$ |
| 13 | $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ | $\phantom{-}\frac{3}{8}e^{10} + \frac{1}{8}e^{9} - \frac{27}{4}e^{8} - \frac{13}{4}e^{7} + \frac{159}{4}e^{6} + \frac{49}{2}e^{5} - \frac{179}{2}e^{4} - \frac{299}{4}e^{3} + \frac{455}{8}e^{2} + \frac{619}{8}e + \frac{85}{4}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 3]$ | $\phantom{-}\frac{3}{4}e^{10} - \frac{1}{2}e^{9} - 13e^{8} + \frac{13}{2}e^{7} + \frac{147}{2}e^{6} - 25e^{5} - 161e^{4} + \frac{33}{2}e^{3} + \frac{491}{4}e^{2} + \frac{45}{2}e - 4$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{3}{4}e^{10} - \frac{1}{4}e^{9} - \frac{53}{4}e^{8} + \frac{9}{4}e^{7} + \frac{307}{4}e^{6} - \frac{5}{4}e^{5} - \frac{691}{4}e^{4} - \frac{145}{4}e^{3} + \frac{259}{2}e^{2} + \frac{131}{2}e + 6$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $-1$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{1}{8}e^{10} + \frac{3}{8}e^{9} + 2e^{8} - 6e^{7} - 10e^{6} + \frac{123}{4}e^{5} + \frac{67}{4}e^{4} - 58e^{3} - \frac{79}{8}e^{2} + \frac{287}{8}e + \frac{45}{4}$ |
| 49 | $[49, 7, -w^{3} + 2w^{2} + 5w - 2]$ | $\phantom{-}\frac{1}{8}e^{10} - \frac{1}{8}e^{9} - 2e^{8} + \frac{7}{4}e^{7} + \frac{19}{2}e^{6} - 8e^{5} - \frac{51}{4}e^{4} + \frac{57}{4}e^{3} - \frac{13}{8}e^{2} - \frac{95}{8}e + \frac{3}{4}$ |
| 49 | $[49, 7, 2w^{3} - 2w^{2} - 9w - 1]$ | $\phantom{-}\frac{1}{4}e^{10} - \frac{3}{4}e^{9} - 4e^{8} + 12e^{7} + \frac{41}{2}e^{6} - 61e^{5} - \frac{81}{2}e^{4} + 110e^{3} + \frac{173}{4}e^{2} - \frac{249}{4}e - \frac{55}{2}$ |
| 53 | $[53, 53, w^{3} - 3w^{2} + 3]$ | $\phantom{-}\frac{1}{4}e^{10} - e^{9} - \frac{7}{2}e^{8} + 16e^{7} + 13e^{6} - 81e^{5} - \frac{11}{2}e^{4} + 144e^{3} - \frac{45}{4}e^{2} - 76e - 9$ |
| 53 | $[53, 53, 2w^{3} - w^{2} - 8w - 3]$ | $\phantom{-}\frac{1}{8}e^{10} + \frac{3}{8}e^{9} - \frac{11}{4}e^{8} - \frac{13}{2}e^{7} + \frac{83}{4}e^{6} + \frac{141}{4}e^{5} - \frac{129}{2}e^{4} - \frac{141}{2}e^{3} + \frac{529}{8}e^{2} + \frac{403}{8}e + \frac{9}{4}$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 6w - 1]$ | $-\frac{3}{4}e^{10} + \frac{1}{4}e^{9} + \frac{51}{4}e^{8} - \frac{7}{4}e^{7} - \frac{277}{4}e^{6} - \frac{19}{4}e^{5} + \frac{561}{4}e^{4} + \frac{227}{4}e^{3} - 89e^{2} - \frac{161}{2}e - 13$ |
| 61 | $[61, 61, -w - 3]$ | $-\frac{1}{8}e^{10} - \frac{13}{8}e^{9} + \frac{13}{4}e^{8} + \frac{111}{4}e^{7} - \frac{105}{4}e^{6} - 151e^{5} + 81e^{4} + \frac{1237}{4}e^{3} - \frac{429}{8}e^{2} - \frac{1715}{8}e - \frac{193}{4}$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 5w - 4]$ | $-\frac{1}{4}e^{10} + \frac{7}{4}e^{9} + \frac{13}{4}e^{8} - 29e^{7} - \frac{41}{4}e^{6} + 153e^{5} - \frac{11}{4}e^{4} - 291e^{3} + \frac{3}{2}e^{2} + \frac{677}{4}e + \frac{85}{2}$ |
| 79 | $[79, 79, w^{3} - 2w^{2} - 4w + 1]$ | $\phantom{-}\frac{3}{8}e^{10} - \frac{9}{8}e^{9} - \frac{25}{4}e^{8} + 18e^{7} + \frac{137}{4}e^{6} - \frac{363}{4}e^{5} - 73e^{4} + 158e^{3} + \frac{547}{8}e^{2} - \frac{585}{8}e - \frac{111}{4}$ |
| 79 | $[79, 79, w^{2} - 5]$ | $-\frac{7}{8}e^{10} + \frac{11}{8}e^{9} + \frac{29}{2}e^{8} - \frac{85}{4}e^{7} - \frac{153}{2}e^{6} + 106e^{5} + \frac{595}{4}e^{4} - \frac{735}{4}e^{3} - \frac{861}{8}e^{2} + \frac{685}{8}e + \frac{151}{4}$ |
| 101 | $[101, 101, w^{3} - 6w]$ | $\phantom{-}\frac{1}{2}e^{9} + \frac{1}{4}e^{8} - \frac{17}{2}e^{7} - \frac{19}{4}e^{6} + 46e^{5} + \frac{95}{4}e^{4} - \frac{193}{2}e^{3} - \frac{165}{4}e^{2} + \frac{137}{2}e + 24$ |
| 101 | $[101, 101, w^{2} - 2w - 4]$ | $-\frac{1}{8}e^{10} + \frac{7}{8}e^{9} + \frac{9}{4}e^{8} - \frac{29}{2}e^{7} - \frac{59}{4}e^{6} + \frac{303}{4}e^{5} + \frac{81}{2}e^{4} - \frac{283}{2}e^{3} - \frac{377}{8}e^{2} + \frac{555}{8}e + \frac{77}{4}$ |
| 103 | $[103, 103, 4w^{3} - 3w^{2} - 20w - 3]$ | $-\frac{5}{4}e^{10} + \frac{5}{4}e^{9} + \frac{43}{2}e^{8} - \frac{69}{4}e^{7} - 120e^{6} + \frac{277}{4}e^{5} + \frac{505}{2}e^{4} - \frac{215}{4}e^{3} - \frac{675}{4}e^{2} - \frac{121}{2}e - 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w^{2} + 2]$ | $1$ |