Properties

Label 2.2.205.1-15.1-a
Base field \(\Q(\sqrt{205}) \)
Weight $[2, 2]$
Level norm $15$
Level $[15, 15, w + 2]$
Dimension $11$
CM no
Base change no

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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: $11$
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:

\(x^{11} - x^{10} - 22x^{9} + 21x^{8} + 171x^{7} - 157x^{6} - 560x^{5} + 488x^{4} + 704x^{3} - 540x^{2} - 224x + 128\)

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Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}1$
4 $[4, 2, 2]$ $...$
5 $[5, 5, -w + 8]$ $-1$
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 $[41, 41, 3w - 22]$ $\phantom{-}\frac{501}{51061}e^{10} - \frac{1298}{51061}e^{9} - \frac{6613}{51061}e^{8} + \frac{21143}{51061}e^{7} + \frac{1383}{51061}e^{6} - \frac{90947}{51061}e^{5} + \frac{239179}{51061}e^{4} + \frac{17996}{51061}e^{3} - \frac{717528}{51061}e^{2} + \frac{209264}{51061}e + \frac{293374}{51061}$
47 $[47, 47, w + 19]$ $-\frac{3017}{102122}e^{10} + \frac{2211}{102122}e^{9} + \frac{33110}{51061}e^{8} - \frac{21735}{102122}e^{7} - \frac{528111}{102122}e^{6} - \frac{42835}{102122}e^{5} + \frac{942785}{51061}e^{4} + \frac{369794}{51061}e^{3} - \frac{1519600}{51061}e^{2} - \frac{631720}{51061}e + \frac{699956}{51061}$
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 $[61, 61, 2w - 13]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 2]$ $-1$
$5$ $[5, 5, -w + 8]$ $1$