Properties

Base field \(\Q(\sqrt{113}) \)
Weight [2, 2]
Level norm 13
Level $[13, 13, -2w + 11]$
Label 2.2.113.1-13.1-b
Dimension 24
CM no
Base change no

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Base field \(\Q(\sqrt{113}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[13, 13, -2w + 11]$
Label 2.2.113.1-13.1-b
Dimension 24
Is CM no
Is base change no
Parent newspace dimension 37

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{24} \) \(\mathstrut -\mathstrut 4x^{23} \) \(\mathstrut -\mathstrut 31x^{22} \) \(\mathstrut +\mathstrut 133x^{21} \) \(\mathstrut +\mathstrut 406x^{20} \) \(\mathstrut -\mathstrut 1898x^{19} \) \(\mathstrut -\mathstrut 2952x^{18} \) \(\mathstrut +\mathstrut 15299x^{17} \) \(\mathstrut +\mathstrut 13203x^{16} \) \(\mathstrut -\mathstrut 77105x^{15} \) \(\mathstrut -\mathstrut 38230x^{14} \) \(\mathstrut +\mathstrut 253803x^{13} \) \(\mathstrut +\mathstrut 74407x^{12} \) \(\mathstrut -\mathstrut 552618x^{11} \) \(\mathstrut -\mathstrut 102701x^{10} \) \(\mathstrut +\mathstrut 786909x^{9} \) \(\mathstrut +\mathstrut 109659x^{8} \) \(\mathstrut -\mathstrut 704841x^{7} \) \(\mathstrut -\mathstrut 95130x^{6} \) \(\mathstrut +\mathstrut 364962x^{5} \) \(\mathstrut +\mathstrut 58858x^{4} \) \(\mathstrut -\mathstrut 90004x^{3} \) \(\mathstrut -\mathstrut 18660x^{2} \) \(\mathstrut +\mathstrut 5397x \) \(\mathstrut +\mathstrut 1223\)

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Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $...$
2 $[2, 2, w + 5]$ $\phantom{-}e$
7 $[7, 7, 6w - 35]$ $...$
7 $[7, 7, -6w - 29]$ $...$
9 $[9, 3, 3]$ $...$
11 $[11, 11, 4w + 19]$ $...$
11 $[11, 11, 4w - 23]$ $...$
13 $[13, 13, -2w + 11]$ $-1$
13 $[13, 13, 2w + 9]$ $...$
25 $[25, 5, -5]$ $...$
31 $[31, 31, 2w - 13]$ $...$
31 $[31, 31, -2w - 11]$ $...$
41 $[41, 41, -8w - 39]$ $...$
41 $[41, 41, 8w - 47]$ $...$
53 $[53, 53, -26w - 125]$ $...$
53 $[53, 53, 26w - 151]$ $...$
61 $[61, 61, -14w + 81]$ $...$
61 $[61, 61, -14w - 67]$ $...$
83 $[83, 83, 2w - 15]$ $...$
83 $[83, 83, -2w - 13]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, -2w + 11]$ $1$