Properties

Label 4014.2.a.d
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + 2q^{5} - 2q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} + 2q^{5} - 2q^{7} - q^{8} - 2q^{10} + 3q^{11} + 2q^{14} + q^{16} - q^{17} - 6q^{19} + 2q^{20} - 3q^{22} + 3q^{23} - q^{25} - 2q^{28} - 5q^{29} + 2q^{31} - q^{32} + q^{34} - 4q^{35} - 7q^{37} + 6q^{38} - 2q^{40} - 3q^{41} + 3q^{44} - 3q^{46} - 2q^{47} - 3q^{49} + q^{50} + q^{53} + 6q^{55} + 2q^{56} + 5q^{58} - 3q^{59} + 6q^{61} - 2q^{62} + q^{64} - 11q^{67} - q^{68} + 4q^{70} + 7q^{73} + 7q^{74} - 6q^{76} - 6q^{77} - 8q^{79} + 2q^{80} + 3q^{82} + 6q^{83} - 2q^{85} - 3q^{88} - 15q^{89} + 3q^{92} + 2q^{94} - 12q^{95} + 12q^{97} + 3q^{98} + O(q^{100}) \)

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 2.00000 0 −2.00000 −1.00000 0 −2.00000
\(n\): 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4014))\):

\( T_{5} - 2 \)
\( T_{7} + 2 \)
\( T_{11} - 3 \)