Properties

Label 2.0.3.1-123627.2-b
Base field \(\Q(\sqrt{-3}) \)
Weight $2$
Level norm $123627$
Level \( \left(-406 a + 203\right) \)
Dimension $1$
CM no
Base change yes
Sign $+1$
Analytic rank \(\ge2\), even

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Base field: \(\Q(\sqrt{-3}) \)

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

Form

Weight: 2
Level: 123627.2 = \( \left(-406 a + 203\right) \)
Level norm: 123627
Dimension: 1
CM: no
Base change: yes 1827.2.a.d , 609.2.a.a
Newspace:2.0.3.1-123627.2 (dimension 33)
Sign of functional equation: $+1$
Analytic rank: \(\ge2\), even

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 3 \) 3.1 = (\( -2 a + 1 \)) \( 1 \)
\( 7 \) 7.1 = (\( -3 a + 1 \)) \( -1 \)
\( 7 \) 7.2 = (\( 3 a - 2 \)) \( -1 \)
\( 841 \) 841.1 = (\( 29 \)) \( -1 \)

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 200 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 4 \) 4.1 = (\( 2 \)) \( -3 \)
\( 13 \) 13.1 = (\( -4 a + 1 \)) \( -2 \)
\( 13 \) 13.2 = (\( 4 a - 3 \)) \( -2 \)
\( 19 \) 19.1 = (\( -5 a + 3 \)) \( -4 \)
\( 19 \) 19.2 = (\( -5 a + 2 \)) \( -4 \)
\( 25 \) 25.1 = (\( 5 \)) \( -6 \)
\( 31 \) 31.1 = (\( -6 a + 1 \)) \( -8 \)
\( 31 \) 31.2 = (\( 6 a - 5 \)) \( -8 \)
\( 37 \) 37.1 = (\( -7 a + 4 \)) \( -10 \)
\( 37 \) 37.2 = (\( -7 a + 3 \)) \( -10 \)
\( 43 \) 43.1 = (\( -7 a + 1 \)) \( 12 \)
\( 43 \) 43.2 = (\( 7 a - 6 \)) \( 12 \)
\( 61 \) 61.1 = (\( -9 a + 5 \)) \( -10 \)
\( 61 \) 61.2 = (\( -9 a + 4 \)) \( -10 \)
\( 67 \) 67.1 = (\( 9 a - 7 \)) \( -12 \)
\( 67 \) 67.2 = (\( 9 a - 2 \)) \( -12 \)
\( 73 \) 73.1 = (\( -9 a + 1 \)) \( 2 \)
\( 73 \) 73.2 = (\( 9 a - 8 \)) \( 2 \)
\( 79 \) 79.1 = (\( 10 a - 7 \)) \( 0 \)
\( 79 \) 79.2 = (\( 10 a - 3 \)) \( 0 \)
\( 97 \) 97.1 = (\( -11 a + 3 \)) \( -6 \)
Display number of eigenvalues