Properties

Label 4.4.19429.1-7.1-c
Base field 4.4.19429.1
Weight $[2, 2, 2, 2]$
Level norm $7$
Level $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$
Dimension $11$
CM no
Base change no

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Base field 4.4.19429.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$
Dimension: $11$
CM: no
Base change: no
Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{11} - 28x^{9} - 12x^{8} + 277x^{7} + 232x^{6} - 1078x^{5} - 1280x^{4} + 1127x^{3} + 1586x^{2} - 288x - 512\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}e$
5 $[5, 5, w]$ $...$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $-1$
13 $[13, 13, -w^{2} + w + 4]$ $...$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $...$
16 $[16, 2, 2]$ $...$
17 $[17, 17, -w + 2]$ $\phantom{-}\frac{739}{3616}e^{10} - \frac{20}{113}e^{9} - \frac{4917}{904}e^{8} + \frac{2215}{904}e^{7} + \frac{186911}{3616}e^{6} - \frac{877}{452}e^{5} - \frac{363057}{1808}e^{4} - \frac{6351}{113}e^{3} + \frac{900565}{3616}e^{2} + \frac{99259}{1808}e - \frac{10215}{113}$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{7183}{96728}e^{10} + \frac{1188}{12091}e^{9} + \frac{46841}{24182}e^{8} - \frac{41057}{24182}e^{7} - \frac{1742475}{96728}e^{6} + \frac{85270}{12091}e^{5} + \frac{3304213}{48364}e^{4} + \frac{27424}{12091}e^{3} - \frac{7801897}{96728}e^{2} - \frac{277603}{48364}e + \frac{324158}{12091}$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $...$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $...$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $-\frac{6105}{96728}e^{10} + \frac{769}{12091}e^{9} + \frac{41811}{24182}e^{8} - \frac{28785}{24182}e^{7} - \frac{1640653}{96728}e^{6} + \frac{73658}{12091}e^{5} + \frac{3346035}{48364}e^{4} - \frac{57644}{12091}e^{3} - \frac{9555815}{96728}e^{2} - \frac{152693}{48364}e + \frac{467262}{12091}$
41 $[41, 41, w^{2} - w - 1]$ $...$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $...$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $-\frac{6105}{96728}e^{10} + \frac{769}{12091}e^{9} + \frac{41811}{24182}e^{8} - \frac{28785}{24182}e^{7} - \frac{1640653}{96728}e^{6} + \frac{73658}{12091}e^{5} + \frac{3346035}{48364}e^{4} - \frac{57644}{12091}e^{3} - \frac{9459087}{96728}e^{2} - \frac{104329}{48364}e + \frac{418898}{12091}$
53 $[53, 53, -w - 3]$ $...$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $...$
59 $[59, 59, 2w^{2} - 3w - 6]$ $-\frac{1101}{24182}e^{10} - \frac{2012}{12091}e^{9} + \frac{16780}{12091}e^{8} + \frac{48914}{12091}e^{7} - \frac{337021}{24182}e^{6} - \frac{399098}{12091}e^{5} + \frac{625005}{12091}e^{4} + \frac{1190582}{12091}e^{3} - \frac{1338323}{24182}e^{2} - \frac{788789}{12091}e + \frac{239892}{12091}$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $...$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $...$
79 $[79, 79, w^{2} - 2w - 1]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $1$