Properties

Label 2.0.4.1-82944.1-l
Base field \(\Q(\sqrt{-1}) \)
Weight $2$
Level norm $82944$
Level \( \left(288\right) \)
Dimension $1$
CM no
Base change yes
Sign $-1$
Analytic rank odd

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

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

Form

Weight: 2
Level: 82944.1 = \( \left(288\right) \)
Level norm: 82944
Dimension: 1
CM: no
Base change: yes 1152.2.a.l , 1152.2.a.i
Newspace:2.0.4.1-82944.1 (dimension 52)
Sign of functional equation: $-1$
Analytic rank: odd

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = \( \left(i + 1\right) \) \( 1 \)
\( 9 \) 9.1 = \( \left(3\right) \) \( 1 \)

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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 5 \) 5.1 = \( \left(-i - 2\right) \) \( 0 \)
\( 5 \) 5.2 = \( \left(2 i + 1\right) \) \( 0 \)
\( 13 \) 13.1 = \( \left(-3 i - 2\right) \) \( 6 \)
\( 13 \) 13.2 = \( \left(2 i + 3\right) \) \( 6 \)
\( 17 \) 17.1 = \( \left(i + 4\right) \) \( -6 \)
\( 17 \) 17.2 = \( \left(i - 4\right) \) \( -6 \)
\( 29 \) 29.1 = \( \left(-2 i + 5\right) \) \( -4 \)
\( 29 \) 29.2 = \( \left(2 i + 5\right) \) \( -4 \)
\( 37 \) 37.1 = \( \left(i + 6\right) \) \( 2 \)
\( 37 \) 37.2 = \( \left(i - 6\right) \) \( 2 \)
\( 41 \) 41.1 = \( \left(-5 i - 4\right) \) \( 2 \)
\( 41 \) 41.2 = \( \left(4 i + 5\right) \) \( 2 \)
\( 49 \) 49.1 = \( \left(7\right) \) \( -10 \)
\( 53 \) 53.1 = \( \left(-2 i + 7\right) \) \( 12 \)
\( 53 \) 53.2 = \( \left(2 i + 7\right) \) \( 12 \)
\( 61 \) 61.1 = \( \left(-6 i - 5\right) \) \( 2 \)
\( 61 \) 61.2 = \( \left(5 i + 6\right) \) \( 2 \)
\( 73 \) 73.1 = \( \left(-3 i - 8\right) \) \( -10 \)
\( 73 \) 73.2 = \( \left(3 i - 8\right) \) \( -10 \)
\( 89 \) 89.1 = \( \left(-5 i + 8\right) \) \( -2 \)
Display number of eigenvalues