Properties

Label 4014.2.a.f
Level 4014
Weight 2
Character orbit 4014.a
Self dual Yes
Analytic conductor 32.052
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4014.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0519513713\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{5} - 4q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + q^{5} - 4q^{7} + q^{8} + q^{10} + 2q^{11} - 6q^{13} - 4q^{14} + q^{16} + 8q^{17} - 6q^{19} + q^{20} + 2q^{22} + 2q^{23} - 4q^{25} - 6q^{26} - 4q^{28} - 4q^{31} + q^{32} + 8q^{34} - 4q^{35} - q^{37} - 6q^{38} + q^{40} + 2q^{41} + 6q^{43} + 2q^{44} + 2q^{46} - 3q^{47} + 9q^{49} - 4q^{50} - 6q^{52} - 14q^{53} + 2q^{55} - 4q^{56} - 10q^{59} - 6q^{61} - 4q^{62} + q^{64} - 6q^{65} - 13q^{67} + 8q^{68} - 4q^{70} - 6q^{71} - 11q^{73} - q^{74} - 6q^{76} - 8q^{77} - 5q^{79} + q^{80} + 2q^{82} + 9q^{83} + 8q^{85} + 6q^{86} + 2q^{88} + 12q^{89} + 24q^{91} + 2q^{92} - 3q^{94} - 6q^{95} + 18q^{97} + 9q^{98} + O(q^{100}) \)

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
1.00000 0 1.00000 1.00000 0 −4.00000 1.00000 0 1.00000
\(n\): 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
\(2\) \(-1\)
\(3\) \(1\)
\(223\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4014))\):

\( T_{5} - 1 \)
\( T_{7} + 4 \)
\( T_{11} - 2 \)