Properties

Label 4032.2.a.k
Level 4032
Weight 2
Character orbit 4032.a
Self dual Yes
Analytic conductor 32.196
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.195682095\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{5} + q^{7} + O(q^{10}) \) \( q - 2q^{5} + q^{7} - 4q^{11} + 2q^{13} + 6q^{17} + 4q^{19} - q^{25} - 2q^{29} - 2q^{35} - 6q^{37} - 2q^{41} - 4q^{43} + q^{49} + 6q^{53} + 8q^{55} - 12q^{59} + 2q^{61} - 4q^{65} + 4q^{67} - 6q^{73} - 4q^{77} + 16q^{79} + 12q^{83} - 12q^{85} + 14q^{89} + 2q^{91} - 8q^{95} + 18q^{97} + O(q^{100}) \)

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 1.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(7\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4032))\):

\( T_{5} + 2 \)
\( T_{11} + 4 \)
\( T_{13} - 2 \)
\( T_{17} - 6 \)
\( T_{19} - 4 \)