Base field 3.3.785.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23, 23, w^{2} - 3]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 3x^{11} - 20x^{10} + 50x^{9} + 171x^{8} - 294x^{7} - 784x^{6} + 648x^{5} + 1884x^{4} - 56x^{3} - 1796x^{2} - 1064x - 176\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-\frac{3}{88}e^{11} + \frac{19}{88}e^{10} + \frac{13}{44}e^{9} - \frac{155}{44}e^{8} - \frac{37}{88}e^{7} + \frac{497}{22}e^{6} + \frac{12}{11}e^{5} - \frac{1501}{22}e^{4} - \frac{238}{11}e^{3} + \frac{873}{11}e^{2} + \frac{1203}{22}e + 7$ |
| 5 | $[5, 5, -w + 3]$ | $-\frac{3}{22}e^{11} + \frac{27}{44}e^{10} + \frac{85}{44}e^{9} - \frac{433}{44}e^{8} - \frac{503}{44}e^{7} + \frac{2579}{44}e^{6} + \frac{477}{11}e^{5} - \frac{6717}{44}e^{4} - \frac{1282}{11}e^{3} + \frac{3035}{22}e^{2} + \frac{3261}{22}e + 32$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}e^{2} - e - 3$ |
| 9 | $[9, 3, w^{2} + w - 4]$ | $-\frac{9}{88}e^{11} + \frac{57}{88}e^{10} + \frac{39}{44}e^{9} - \frac{465}{44}e^{8} - \frac{67}{88}e^{7} + \frac{729}{11}e^{6} - \frac{30}{11}e^{5} - \frac{4173}{22}e^{4} - \frac{889}{22}e^{3} + \frac{2223}{11}e^{2} + \frac{2839}{22}e + 22$ |
| 13 | $[13, 13, w + 3]$ | $-\frac{1}{4}e^{8} + \frac{5}{4}e^{7} + 2e^{6} - \frac{29}{2}e^{5} - \frac{17}{4}e^{4} + 54e^{3} + \frac{15}{2}e^{2} - \frac{127}{2}e - 23$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{31}{88}e^{11} + \frac{123}{88}e^{10} + \frac{62}{11}e^{9} - \frac{251}{11}e^{8} - \frac{3301}{88}e^{7} + \frac{1499}{11}e^{6} + \frac{6249}{44}e^{5} - \frac{7627}{22}e^{4} - \frac{3585}{11}e^{3} + \frac{6371}{22}e^{2} + \frac{7679}{22}e + 82$ |
| 23 | $[23, 23, w^{2} - 2]$ | $-\frac{3}{44}e^{11} - \frac{3}{44}e^{10} + \frac{23}{11}e^{9} + \frac{16}{11}e^{8} - \frac{939}{44}e^{7} - \frac{337}{22}e^{6} + \frac{1003}{11}e^{5} + \frac{1673}{22}e^{4} - \frac{1587}{11}e^{3} - \frac{1510}{11}e^{2} + \frac{235}{11}e + 22$ |
| 23 | $[23, 23, w^{2} - 3]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{2} + 8]$ | $\phantom{-}\frac{13}{88}e^{11} - \frac{31}{88}e^{10} - \frac{137}{44}e^{9} + \frac{261}{44}e^{8} + \frac{2221}{88}e^{7} - \frac{1429}{44}e^{6} - \frac{4245}{44}e^{5} + \frac{2577}{44}e^{4} + \frac{1794}{11}e^{3} + \frac{12}{11}e^{2} - \frac{874}{11}e - 28$ |
| 29 | $[29, 29, w - 4]$ | $-\frac{3}{11}e^{11} + \frac{8}{11}e^{10} + \frac{225}{44}e^{9} - \frac{235}{22}e^{8} - \frac{1699}{44}e^{7} + \frac{1105}{22}e^{6} + \frac{6203}{44}e^{5} - \frac{3017}{44}e^{4} - \frac{4853}{22}e^{3} - \frac{353}{11}e^{2} + \frac{1583}{22}e + 19$ |
| 37 | $[37, 37, w^{2} + w - 8]$ | $-\frac{3}{88}e^{11} - \frac{3}{88}e^{10} + \frac{23}{22}e^{9} + \frac{21}{44}e^{8} - \frac{829}{88}e^{7} - \frac{249}{44}e^{6} + \frac{673}{22}e^{5} + \frac{765}{22}e^{4} - \frac{311}{22}e^{3} - \frac{733}{11}e^{2} - \frac{1283}{22}e - 11$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $-\frac{27}{88}e^{11} + \frac{83}{88}e^{10} + \frac{119}{22}e^{9} - \frac{159}{11}e^{8} - \frac{3325}{88}e^{7} + \frac{823}{11}e^{6} + \frac{5613}{44}e^{5} - \frac{3103}{22}e^{4} - \frac{4141}{22}e^{3} + \frac{1205}{22}e^{2} + \frac{1345}{22}e + 3$ |
| 47 | $[47, 47, 2w^{2} + w - 8]$ | $\phantom{-}\frac{27}{88}e^{11} - \frac{105}{88}e^{10} - \frac{119}{22}e^{9} + \frac{461}{22}e^{8} + \frac{3523}{88}e^{7} - \frac{5965}{44}e^{6} - \frac{3703}{22}e^{5} + \frac{16535}{44}e^{4} + \frac{9311}{22}e^{3} - \frac{7453}{22}e^{2} - \frac{5353}{11}e - 122$ |
| 59 | $[59, 59, -2w^{2} - 3w + 6]$ | $-\frac{17}{88}e^{11} + \frac{49}{88}e^{10} + \frac{169}{44}e^{9} - \frac{199}{22}e^{8} - \frac{2857}{88}e^{7} + \frac{1159}{22}e^{6} + \frac{1564}{11}e^{5} - \frac{5377}{44}e^{4} - \frac{3413}{11}e^{3} + \frac{1369}{22}e^{2} + \frac{2886}{11}e + 84$ |
| 61 | $[61, 61, -2w - 1]$ | $-\frac{13}{88}e^{11} + \frac{53}{88}e^{10} + \frac{115}{44}e^{9} - \frac{481}{44}e^{8} - \frac{1671}{88}e^{7} + \frac{800}{11}e^{6} + \frac{855}{11}e^{5} - \frac{4539}{22}e^{4} - \frac{4303}{22}e^{3} + \frac{2144}{11}e^{2} + \frac{5169}{22}e + 50$ |
| 67 | $[67, 67, -2w - 3]$ | $-\frac{17}{88}e^{11} + \frac{49}{88}e^{10} + \frac{79}{22}e^{9} - \frac{387}{44}e^{8} - \frac{2329}{88}e^{7} + \frac{519}{11}e^{6} + \frac{4221}{44}e^{5} - \frac{4101}{44}e^{4} - \frac{3691}{22}e^{3} + \frac{360}{11}e^{2} + \frac{1225}{11}e + 36$ |
| 79 | $[79, 79, 2w^{2} - 9]$ | $\phantom{-}\frac{45}{88}e^{11} - \frac{131}{88}e^{10} - \frac{415}{44}e^{9} + \frac{1005}{44}e^{8} + \frac{6253}{88}e^{7} - \frac{5307}{44}e^{6} - \frac{11577}{44}e^{5} + \frac{10413}{44}e^{4} + \frac{4802}{11}e^{3} - \frac{1028}{11}e^{2} - \frac{2252}{11}e - 30$ |
| 109 | $[109, 109, w^{2} + 2w - 6]$ | $-\frac{39}{88}e^{11} + \frac{71}{88}e^{10} + \frac{211}{22}e^{9} - \frac{519}{44}e^{8} - \frac{7059}{88}e^{7} + \frac{541}{11}e^{6} + \frac{13439}{44}e^{5} - \frac{757}{44}e^{4} - \frac{10093}{22}e^{3} - \frac{1895}{11}e^{2} + \frac{1016}{11}e + 34$ |
| 109 | $[109, 109, 2w^{2} + w - 14]$ | $-\frac{13}{88}e^{11} + \frac{9}{88}e^{10} + \frac{159}{44}e^{9} - \frac{19}{44}e^{8} - \frac{2991}{88}e^{7} - \frac{237}{22}e^{6} + \frac{3107}{22}e^{5} + \frac{1973}{22}e^{4} - \frac{4809}{22}e^{3} - \frac{2091}{11}e^{2} + \frac{615}{22}e + 26$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, w^{2} - 3]$ | $-1$ |