Properties

Label 2.0.3.1-136900.2-e
Base field \(\Q(\sqrt{-3}) \)
Weight $2$
Level norm $136900$
Level \( \left(370\right) \)
Dimension $1$
CM no
Base change yes
Sign $-1$
Analytic rank odd

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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: 136900.2 = \( \left(370\right) \)
Level norm: 136900
Dimension: 1
CM: no
Base change: yes 3330.2.a.w , 370.2.a.b
Newspace:2.0.3.1-136900.2 (dimension 13)
Sign of functional equation: $-1$
Analytic rank: odd

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 4 \) 4.1 = \( \left(2\right) \) \( -1 \)
\( 25 \) 25.1 = \( \left(5\right) \) \( -1 \)
\( 37 \) 37.1 = \( \left(-3 a + 7\right) \) \( 1 \)
\( 37 \) 37.2 = \( \left(3 a + 4\right) \) \( 1 \)

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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 3 \) 3.1 = \( \left(a + 1\right) \) \( 0 \)
\( 7 \) 7.1 = \( \left(-a - 2\right) \) \( 0 \)
\( 7 \) 7.2 = \( \left(a - 3\right) \) \( 0 \)
\( 13 \) 13.1 = \( \left(a + 3\right) \) \( 2 \)
\( 13 \) 13.2 = \( \left(a - 4\right) \) \( 2 \)
\( 19 \) 19.1 = \( \left(-2 a + 5\right) \) \( -4 \)
\( 19 \) 19.2 = \( \left(2 a + 3\right) \) \( -4 \)
\( 31 \) 31.1 = \( \left(a + 5\right) \) \( -4 \)
\( 31 \) 31.2 = \( \left(a - 6\right) \) \( -4 \)
\( 43 \) 43.1 = \( \left(a + 6\right) \) \( 4 \)
\( 43 \) 43.2 = \( \left(a - 7\right) \) \( 4 \)
\( 61 \) 61.1 = \( \left(-4 a + 9\right) \) \( 10 \)
\( 61 \) 61.2 = \( \left(4 a + 5\right) \) \( 10 \)
\( 67 \) 67.1 = \( \left(-2 a + 9\right) \) \( -8 \)
\( 67 \) 67.2 = \( \left(2 a + 7\right) \) \( -8 \)
\( 73 \) 73.1 = \( \left(a + 8\right) \) \( 10 \)
\( 73 \) 73.2 = \( \left(a - 9\right) \) \( 10 \)
\( 79 \) 79.1 = \( \left(-3 a + 10\right) \) \( -4 \)
\( 79 \) 79.2 = \( \left(3 a + 7\right) \) \( -4 \)
\( 97 \) 97.1 = \( \left(-3 a - 8\right) \) \( 6 \)
Display number of eigenvalues