Properties

Label 1006.2.a.a
Level 1006
Weight 2
Character orbit 1006.a
Self dual Yes
Analytic conductor 8.033
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 1006 = 2 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1006.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(8.03295044334\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{8} - 3q^{9} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{8} - 3q^{9} + 4q^{11} + 2q^{13} + q^{16} - 2q^{17} + 3q^{18} - 2q^{19} - 4q^{22} + 8q^{23} - 5q^{25} - 2q^{26} + 8q^{31} - q^{32} + 2q^{34} - 3q^{36} + 8q^{37} + 2q^{38} + 6q^{41} + 4q^{43} + 4q^{44} - 8q^{46} - 8q^{47} - 7q^{49} + 5q^{50} + 2q^{52} + 12q^{53} - 4q^{59} + 2q^{61} - 8q^{62} + q^{64} - 4q^{67} - 2q^{68} + 4q^{71} + 3q^{72} - 6q^{73} - 8q^{74} - 2q^{76} + 8q^{79} + 9q^{81} - 6q^{82} + 12q^{83} - 4q^{86} - 4q^{88} + 18q^{89} + 8q^{92} + 8q^{94} - 6q^{97} + 7q^{98} - 12q^{99} + O(q^{100}) \)

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
−1.00000 0 1.00000 0 0 0 −1.00000 −3.00000 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1006))\):

\( T_{3} \)
\( T_{5} \)