Base field \(\Q(\sqrt{205}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[15, 15, w + 2]$ |
| Dimension: | $28$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $100$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{28} + 53x^{26} + 1212x^{24} + 15683x^{22} + 126655x^{20} + 665277x^{18} + 2306164x^{16} + 5280412x^{14} + 7943984x^{12} + 7752824x^{10} + 4765216x^{8} + 1730512x^{6} + 322912x^{4} + 21648x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 5 | $[5, 5, -w + 8]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 13 | $[13, 13, w + 3]$ | $...$ |
| 13 | $[13, 13, w + 9]$ | $...$ |
| 17 | $[17, 17, w]$ | $...$ |
| 17 | $[17, 17, w + 16]$ | $...$ |
| 31 | $[31, 31, -w - 4]$ | $...$ |
| 31 | $[31, 31, w - 5]$ | $...$ |
| 41 | $[41, 41, 3w - 22]$ | $...$ |
| 47 | $[47, 47, w + 19]$ | $...$ |
| 47 | $[47, 47, w + 27]$ | $...$ |
| 53 | $[53, 53, w + 14]$ | $...$ |
| 53 | $[53, 53, w + 38]$ | $...$ |
| 59 | $[59, 59, -w - 10]$ | $...$ |
| 59 | $[59, 59, w - 11]$ | $...$ |
| 61 | $[61, 61, 2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 2]$ | $\frac{1044318246797}{54698742050752}e^{27} + \frac{54294605347941}{54698742050752}e^{25} + \frac{151369433234479}{6837342756344}e^{23} + \frac{15157947884580943}{54698742050752}e^{21} + \frac{117010271987362399}{54698742050752}e^{19} + \frac{577077702801269869}{54698742050752}e^{17} + \frac{28567168603714811}{854667844543}e^{15} + \frac{919138111747295317}{13674685512688}e^{13} + \frac{143587672992425169}{1709335689086}e^{11} + \frac{431072370477280669}{6837342756344}e^{9} + \frac{90217177311707281}{3418671378172}e^{7} + \frac{17443188036453445}{3418671378172}e^{5} + \frac{359341007195591}{1709335689086}e^{3} - \frac{20915945993651}{3418671378172}e$ |
| $5$ | $[5, 5, -w + 8]$ | $-1$ |