Base field \(\Q(\sqrt{305}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8,8,-w + 4]$ |
| Dimension: | $46$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $92$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{46} + 74x^{44} + 2543x^{42} + 53904x^{40} + 789545x^{38} + 8484233x^{36} + 69309333x^{34} + 440153332x^{32} + 2203555245x^{30} + 8768068972x^{28} + 27832559066x^{26} + 70474088061x^{24} + 141822029731x^{22} + 225170231756x^{20} + 278833847784x^{18} + 264882937899x^{16} + 188593673930x^{14} + 97393078926x^{12} + 34800847715x^{10} + 8022536787x^{8} + 1071894140x^{6} + 70607655x^{4} + 1762455x^{2} + 9409\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -4w + 37]$ | $...$ |
| 7 | $[7, 7, w + 2]$ | $...$ |
| 7 | $[7, 7, w + 4]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 17 | $[17, 17, w + 6]$ | $...$ |
| 17 | $[17, 17, w + 10]$ | $...$ |
| 19 | $[19, 19, -2w + 19]$ | $...$ |
| 19 | $[19, 19, -2w - 17]$ | $...$ |
| 23 | $[23, 23, w + 5]$ | $...$ |
| 23 | $[23, 23, w + 17]$ | $...$ |
| 37 | $[37, 37, w + 1]$ | $...$ |
| 37 | $[37, 37, w + 35]$ | $...$ |
| 41 | $[41, 41, -22w + 203]$ | $...$ |
| 41 | $[41, 41, -6w + 55]$ | $...$ |
| 43 | $[43, 43, w + 20]$ | $...$ |
| 43 | $[43, 43, w + 22]$ | $...$ |
| 53 | $[53, 53, w + 13]$ | $...$ |
| 53 | $[53, 53, w + 39]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 2]$ | $-\frac{5446973061864690008741}{5385130927768554785572864}e^{45} - \frac{383387935778731355684683}{5385130927768554785572864}e^{43} - \frac{6232846325907398821554761}{2692565463884277392786432}e^{41} - \frac{124270757001178890777823077}{2692565463884277392786432}e^{39} - \frac{3401775779893994131798692959}{5385130927768554785572864}e^{37} - \frac{4238410805022113342143701805}{673141365971069348196608}e^{35} - \frac{254820091728881652151897468417}{5385130927768554785572864}e^{33} - \frac{1474913122307953608302463915001}{5385130927768554785572864}e^{31} - \frac{3329735469684261546922699183151}{2692565463884277392786432}e^{29} - \frac{11807350714111909160844943676993}{2692565463884277392786432}e^{27} - \frac{16473675275125180043816216469271}{1346282731942138696393216}e^{25} - \frac{144367447797073448335959640182381}{5385130927768554785572864}e^{23} - \frac{3855492209155470553595823103789}{84142670746383668524576}e^{21} - \frac{81358564753765433104448560796447}{1346282731942138696393216}e^{19} - \frac{81444483959705914696966779324685}{1346282731942138696393216}e^{17} - \frac{241709816814585050023355052924539}{5385130927768554785572864}e^{15} - \frac{128424779154623234864648960090169}{5385130927768554785572864}e^{13} - \frac{46436396350083455787905874660947}{5385130927768554785572864}e^{11} - \frac{5277994375707877594255617517527}{2692565463884277392786432}e^{9} - \frac{1321028950179796137790111260693}{5385130927768554785572864}e^{7} - \frac{70440734099916158102440485797}{5385130927768554785572864}e^{5} - \frac{75329870166096804270459663}{1346282731942138696393216}e^{3} + \frac{64479033297131241666643281}{5385130927768554785572864}e$ |