Properties

Label 2.0.4.1-1025.2-a2
Base field \(\Q(\sqrt{-1}) \)
Weight $2$
Level norm $1025$
Level \( \left(i + 32\right) \)
Dimension $2$
CM not determined
Base change no
Sign not determined
Analytic rank not determined

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

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

Form

Weight: 2
Level: 1025.2 = \( \left(i + 32\right) \)
Level norm: 1025
Dimension: 2
CM: not determined
Base change: no
Newspace:2.0.4.1-1025.2 (dimension 2)
Sign of functional equation: not determined
Analytic rank: not determined
L-ratio: not determined

Atkin-Lehner eigenvalues

Not known

Hecke eigenvalues

The Hecke eigenfield is \(\Q(z)\) where $z$ is a root of the defining polynomial: \( x^{2} - 5 \). The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 15 eigenvalues, all of which are displayed below. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 2 \) 2.1 = (\( i + 1 \)) \( \frac{1}{2} z + \frac{1}{2} \)
\( 5 \) 5.2 = (\( 2 i + 1 \)) \( -z + 1 \)
\( 9 \) 9.1 = (\( 3 \)) \( 0 \)
\( 13 \) 13.1 = (\( -3 i - 2 \)) \( z - 1 \)
\( 13 \) 13.2 = (\( 2 i + 3 \)) \( -2 z - 1 \)
\( 17 \) 17.1 = (\( i + 4 \)) \( z + 3 \)
\( 17 \) 17.2 = (\( i - 4 \)) \( -2 z + 3 \)
\( 29 \) 29.1 = (\( -2 i + 5 \)) \( 2 z \)
\( 29 \) 29.2 = (\( 2 i + 5 \)) \( -2 z + 5 \)
\( 37 \) 37.1 = (\( i + 6 \)) \( 3 z + 3 \)
\( 37 \) 37.2 = (\( i - 6 \)) \( -2 \)
\( 41 \) 41.1 = (\( -5 i - 4 \)) \( -3 \)
\( 49 \) 49.1 = (\( 7 \)) \( -3 z - 5 \)
Display number of eigenvalues