Properties

Label 4024.2.a.c
Level 4024
Weight 2
Character orbit 4024.a
Self dual Yes
Analytic conductor 32.132
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4024 = 2^{3} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1318017734\)
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

\(f(q)\) \(=\) \( q - q^{3} + 2q^{5} + q^{7} - 2q^{9} + O(q^{10}) \) \( q - q^{3} + 2q^{5} + q^{7} - 2q^{9} + 3q^{11} + 3q^{13} - 2q^{15} - 2q^{17} - q^{21} - 3q^{23} - q^{25} + 5q^{27} + 6q^{29} + 4q^{31} - 3q^{33} + 2q^{35} + 8q^{37} - 3q^{39} - 12q^{41} + 7q^{43} - 4q^{45} + 3q^{47} - 6q^{49} + 2q^{51} + 12q^{53} + 6q^{55} + 8q^{59} - 5q^{61} - 2q^{63} + 6q^{65} - 9q^{67} + 3q^{69} + 4q^{71} - 10q^{73} + q^{75} + 3q^{77} + q^{81} + 3q^{83} - 4q^{85} - 6q^{87} - 2q^{89} + 3q^{91} - 4q^{93} + 14q^{97} - 6q^{99} + O(q^{100}) \)

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 −1.00000 0 2.00000 0 1.00000 0 −2.00000 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
\(2\) \(1\)
\(503\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4024))\):

\( T_{3} + 1 \)
\( T_{5} - 2 \)
\( T_{7} - 1 \)