Properties

Label 4014.2.a.c
Level 4014
Weight 2
Character orbit 4014.a
Self dual Yes
Analytic conductor 32.052
Analytic rank 0
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: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{8} + 2q^{11} + 4q^{13} + q^{16} + 2q^{17} + 8q^{19} - 2q^{22} + 8q^{23} - 5q^{25} - 4q^{26} + 6q^{29} + 8q^{31} - q^{32} - 2q^{34} - 6q^{37} - 8q^{38} - 10q^{41} - 12q^{43} + 2q^{44} - 8q^{46} - 7q^{49} + 5q^{50} + 4q^{52} - 6q^{53} - 6q^{58} + 10q^{59} + 4q^{61} - 8q^{62} + q^{64} - 6q^{67} + 2q^{68} - 4q^{71} + 10q^{73} + 6q^{74} + 8q^{76} + 12q^{79} + 10q^{82} - 8q^{83} + 12q^{86} - 2q^{88} + 2q^{89} + 8q^{92} - 10q^{97} + 7q^{98} + O(q^{100}) \)

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4014))\):

\( T_{5} \)
\( T_{7} \)
\( T_{11} - 2 \)