Properties

Base field \(\Q(\sqrt{393}) \)
Weight [2, 2]
Level norm 7
Level $[7, 7, -2w + 21]$
Label 2.2.393.1-7.1-a
Dimension 54
CM no
Base change no

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Base field \(\Q(\sqrt{393}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 98\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[7, 7, -2w + 21]$
Label 2.2.393.1-7.1-a
Dimension 54
Is CM no
Is base change no
Parent newspace dimension 128

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{54} \) \(\mathstrut -\mathstrut 75x^{52} \) \(\mathstrut +\mathstrut 2635x^{50} \) \(\mathstrut -\mathstrut 57651x^{48} \) \(\mathstrut +\mathstrut 880833x^{46} \) \(\mathstrut -\mathstrut 9989610x^{44} \) \(\mathstrut +\mathstrut 87265381x^{42} \) \(\mathstrut -\mathstrut 601442916x^{40} \) \(\mathstrut +\mathstrut 3323302968x^{38} \) \(\mathstrut -\mathstrut 14880425680x^{36} \) \(\mathstrut +\mathstrut 54362720209x^{34} \) \(\mathstrut -\mathstrut 162667177340x^{32} \) \(\mathstrut +\mathstrut 399220394480x^{30} \) \(\mathstrut -\mathstrut 802972530011x^{28} \) \(\mathstrut +\mathstrut 1319932283119x^{26} \) \(\mathstrut -\mathstrut 1764811820217x^{24} \) \(\mathstrut +\mathstrut 1906324745071x^{22} \) \(\mathstrut -\mathstrut 1648792826154x^{20} \) \(\mathstrut +\mathstrut 1128975002006x^{18} \) \(\mathstrut -\mathstrut 603425621805x^{16} \) \(\mathstrut +\mathstrut 247388317534x^{14} \) \(\mathstrut -\mathstrut 76101844080x^{12} \) \(\mathstrut +\mathstrut 17072462598x^{10} \) \(\mathstrut -\mathstrut 2686844874x^{8} \) \(\mathstrut +\mathstrut 280395629x^{6} \) \(\mathstrut -\mathstrut 17757387x^{4} \) \(\mathstrut +\mathstrut 584936x^{2} \) \(\mathstrut -\mathstrut 7356\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -17w - 160]$ $\phantom{-}e$
2 $[2, 2, -17w + 177]$ $...$
3 $[3, 3, -842w + 8767]$ $...$
7 $[7, 7, -2w + 21]$ $\phantom{-}1$
7 $[7, 7, 2w + 19]$ $...$
13 $[13, 13, -12w - 113]$ $...$
13 $[13, 13, 12w - 125]$ $...$
17 $[17, 17, 182w - 1895]$ $...$
17 $[17, 17, 182w + 1713]$ $...$
23 $[23, 23, -512w - 4819]$ $...$
23 $[23, 23, 512w - 5331]$ $...$
25 $[25, 5, -5]$ $...$
29 $[29, 29, 22w - 229]$ $...$
29 $[29, 29, 22w + 207]$ $...$
43 $[43, 43, 114w + 1073]$ $...$
43 $[43, 43, 114w - 1187]$ $...$
47 $[47, 47, 8w - 83]$ $...$
47 $[47, 47, -8w - 75]$ $...$
61 $[61, 61, -1172w - 11031]$ $...$
61 $[61, 61, 1172w - 12203]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, -2w + 21]$ $-1$