Properties

Label 32.2.a.a
Level 32
Weight 2
Character orbit 32.a
Self dual Yes
Analytic conductor 0.256
Analytic rank 0
Dimension 1
CM disc. -4
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 32.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.255521286468\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut -\mathstrut 10q^{29} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 7q^{49} \) \(\mathstrut +\mathstrut 14q^{53} \) \(\mathstrut -\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 0 0 −2.00000 0 0 0 −3.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
4.b Odd 1 CM by \(\Q(\sqrt{-1}) \) yes

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\).