Base field \(\Q(\sqrt{197}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[23,23,-w + 9]$ |
| Dimension: | $43$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $81$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{43} + x^{42} - 107x^{41} - 99x^{40} + 5241x^{39} + 4485x^{38} - 155769x^{37} - 123524x^{36} + 3139252x^{35} + 2317834x^{34} - 45408975x^{33} - 31472838x^{32} + 486755778x^{31} + 320524340x^{30} - 3936468390x^{29} - 2502154113x^{28} + 24224789798x^{27} + 15152766533x^{26} - 113612777248x^{25} - 71456797540x^{24} + 404182681269x^{23} + 261401784490x^{22} - 1078900632199x^{21} - 733521886572x^{20} + 2122148793234x^{19} + 1550076768340x^{18} - 2991079606593x^{17} - 2404324635504x^{16} + 2889688891017x^{15} + 2646278115486x^{14} - 1764399735113x^{13} - 1973838845927x^{12} + 551685723463x^{11} + 930522569120x^{10} + 1896113944x^{9} - 243160998066x^{8} - 53416477930x^{7} + 24121560188x^{6} + 11263533068x^{5} + 1002782647x^{4} - 177217223x^{3} - 30288781x^{2} + 195578x + 151276\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 7]$ | $...$ |
| 7 | $[7, 7, w + 6]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 19 | $[19, 19, w + 5]$ | $...$ |
| 19 | $[19, 19, w - 6]$ | $...$ |
| 23 | $[23, 23, w + 8]$ | $...$ |
| 23 | $[23, 23, -w + 9]$ | $-1$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 29 | $[29, 29, -w - 4]$ | $...$ |
| 29 | $[29, 29, w - 5]$ | $...$ |
| 37 | $[37, 37, -w - 3]$ | $...$ |
| 37 | $[37, 37, w - 4]$ | $...$ |
| 41 | $[41, 41, -w - 9]$ | $...$ |
| 41 | $[41, 41, w - 10]$ | $...$ |
| 43 | $[43, 43, -w - 2]$ | $...$ |
| 43 | $[43, 43, w - 3]$ | $...$ |
| 47 | $[47, 47, -w - 1]$ | $...$ |
| 47 | $[47, 47, w - 2]$ | $...$ |
| 53 | $[53, 53, 2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23,23,-w + 9]$ | $1$ |