Properties

Label 4014.2.a.e
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

Related objects

Downloads

Learn more about

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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + q^{8} - q^{11} - 2q^{13} + q^{16} - q^{17} - 4q^{19} - q^{22} - q^{23} - 5q^{25} - 2q^{26} + 3q^{29} - 10q^{31} + q^{32} - q^{34} - 3q^{37} - 4q^{38} + 5q^{41} - 6q^{43} - q^{44} - q^{46} - 6q^{47} - 7q^{49} - 5q^{50} - 2q^{52} + 9q^{53} + 3q^{58} + q^{59} + 4q^{61} - 10q^{62} + q^{64} + 9q^{67} - q^{68} - 4q^{71} - 5q^{73} - 3q^{74} - 4q^{76} + 5q^{82} - 14q^{83} - 6q^{86} - q^{88} + 5q^{89} - q^{92} - 6q^{94} + 2q^{97} - 7q^{98} + O(q^{100}) \)

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 0 0 0 1.00000 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
\(2\) \(-1\)
\(3\) \(-1\)
\(223\) \(1\)

Hecke kernels

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

\( T_{5} \)
\( T_{7} \)
\( T_{11} + 1 \)