Properties

Label 1001.2.a.c
Level 1001
Weight 2
Character orbit 1001.a
Self dual Yes
Analytic conductor 7.993
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(7.99302524233\)
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

\(f(q)\) \(=\) \( q + 2q^{3} - 2q^{4} - q^{5} - q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{3} - 2q^{4} - q^{5} - q^{7} + q^{9} - q^{11} - 4q^{12} - q^{13} - 2q^{15} + 4q^{16} + 2q^{17} - q^{19} + 2q^{20} - 2q^{21} - 5q^{23} - 4q^{25} - 4q^{27} + 2q^{28} - 5q^{29} - 9q^{31} - 2q^{33} + q^{35} - 2q^{36} + 10q^{37} - 2q^{39} - 2q^{41} - 13q^{43} + 2q^{44} - q^{45} - 7q^{47} + 8q^{48} + q^{49} + 4q^{51} + 2q^{52} - q^{53} + q^{55} - 2q^{57} + 8q^{59} + 4q^{60} - 2q^{61} - q^{63} - 8q^{64} + q^{65} + 2q^{67} - 4q^{68} - 10q^{69} + 6q^{71} + 5q^{73} - 8q^{75} + 2q^{76} + q^{77} + 11q^{79} - 4q^{80} - 11q^{81} - 3q^{83} + 4q^{84} - 2q^{85} - 10q^{87} + 5q^{89} + q^{91} + 10q^{92} - 18q^{93} + q^{95} + 5q^{97} - q^{99} + O(q^{100}) \)

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
0 2.00000 −2.00000 −1.00000 0 −1.00000 0 1.00000 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
\(7\) \(1\)
\(11\) \(1\)
\(13\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1001))\):

\( T_{2} \)
\( T_{3} - 2 \)