Properties

Label 2.2.205.1-15.1-e
Base field \(\Q(\sqrt{205}) \)
Weight $[2, 2]$
Level norm $15$
Level $[15, 15, w + 2]$
Dimension $22$
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: $22$
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:

\(x^{22} + 45x^{20} + 868x^{18} + 9399x^{16} + 62859x^{14} + 269169x^{12} + 740392x^{10} + 1278168x^{8} + 1313728x^{6} + 731920x^{4} + 188416x^{2} + 16384\)

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Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $...$
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 $[41, 41, 3w - 22]$ $...$
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 $[61, 61, 2w - 13]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 2]$ $-\frac{49131}{184889344}e^{21} - \frac{1529263}{184889344}e^{19} - \frac{4136171}{46222336}e^{17} - \frac{46653309}{184889344}e^{15} + \frac{479228103}{184889344}e^{13} + \frac{4843332133}{184889344}e^{11} + \frac{2354735517}{23111168}e^{9} + \frac{4676427319}{23111168}e^{7} + \frac{590535047}{2888896}e^{5} + \frac{1065961029}{11555584}e^{3} + \frac{4742301}{361112}e$
$5$ $[5, 5, -w + 8]$ $1$