Properties

Label 2.0.4.1-882.1-a
Base field \(\Q(\sqrt{-1}) \)
Weight $2$
Level norm $882$
Level \( \left(21 i + 21\right) \)
Dimension $1$
CM no
Base change yes
Sign $+1$
Analytic rank \(0\)

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Base field: \(\Q(\sqrt{-1}) \)

Generator \(i\), with minimal polynomial \(x^2 + 1\); class number \(1\).

Form

Weight: 2
Level: 882.1 = \( \left(21 i + 21\right) \)
Level norm: 882
Dimension: 1
CM: no
Base change: yes 336.2.a.d , 42.2.a.a
Newspace:2.0.4.1-882.1 (dimension 3)
Sign of functional equation: $+1$
Analytic rank: \(0\)
L-ratio: 1/2

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( i + 1 \)) \( -1 \)
\( 9 \) 9.1 = (\( 3 \)) \( -1 \)
\( 49 \) 49.1 = (\( 7 \)) \( -1 \)

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 1000 eigenvalues, of which 20 are currently shown below. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 5 \) 5.1 = (\( -i - 2 \)) \( -2 \)
\( 5 \) 5.2 = (\( 2 i + 1 \)) \( -2 \)
\( 13 \) 13.1 = (\( -3 i - 2 \)) \( 6 \)
\( 13 \) 13.2 = (\( 2 i + 3 \)) \( 6 \)
\( 17 \) 17.1 = (\( i + 4 \)) \( 2 \)
\( 17 \) 17.2 = (\( i - 4 \)) \( 2 \)
\( 29 \) 29.1 = (\( -2 i + 5 \)) \( -2 \)
\( 29 \) 29.2 = (\( 2 i + 5 \)) \( -2 \)
\( 37 \) 37.1 = (\( i + 6 \)) \( -10 \)
\( 37 \) 37.2 = (\( i - 6 \)) \( -10 \)
\( 41 \) 41.1 = (\( -5 i - 4 \)) \( -6 \)
\( 41 \) 41.2 = (\( 4 i + 5 \)) \( -6 \)
\( 53 \) 53.1 = (\( -2 i + 7 \)) \( 6 \)
\( 53 \) 53.2 = (\( 2 i + 7 \)) \( 6 \)
\( 61 \) 61.1 = (\( -6 i - 5 \)) \( 6 \)
\( 61 \) 61.2 = (\( 5 i + 6 \)) \( 6 \)
\( 73 \) 73.1 = (\( -3 i - 8 \)) \( 10 \)
\( 73 \) 73.2 = (\( 3 i - 8 \)) \( 10 \)
\( 89 \) 89.1 = (\( -5 i + 8 \)) \( -6 \)
\( 89 \) 89.2 = (\( -8 i + 5 \)) \( -6 \)
Display number of eigenvalues