Properties

Label 1001.2.a.b
Level 1001
Weight 2
Character orbit 1001.a
Self dual Yes
Analytic conductor 7.993
Analytic rank 0
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: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{4} - 2q^{5} - q^{7} + 3q^{8} - 3q^{9} + O(q^{10}) \) \( q - q^{2} - q^{4} - 2q^{5} - q^{7} + 3q^{8} - 3q^{9} + 2q^{10} + q^{11} - q^{13} + q^{14} - q^{16} - 2q^{17} + 3q^{18} - 4q^{19} + 2q^{20} - q^{22} - q^{25} + q^{26} + q^{28} + 6q^{29} - 4q^{31} - 5q^{32} + 2q^{34} + 2q^{35} + 3q^{36} + 6q^{37} + 4q^{38} - 6q^{40} + 6q^{41} + 12q^{43} - q^{44} + 6q^{45} + 4q^{47} + q^{49} + q^{50} + q^{52} - 10q^{53} - 2q^{55} - 3q^{56} - 6q^{58} + 10q^{61} + 4q^{62} + 3q^{63} + 7q^{64} + 2q^{65} + 12q^{67} + 2q^{68} - 2q^{70} - 9q^{72} + 14q^{73} - 6q^{74} + 4q^{76} - q^{77} + 2q^{80} + 9q^{81} - 6q^{82} - 4q^{83} + 4q^{85} - 12q^{86} + 3q^{88} - 14q^{89} - 6q^{90} + q^{91} - 4q^{94} + 8q^{95} - 14q^{97} - q^{98} - 3q^{99} + O(q^{100}) \)

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 −2.00000 0 −1.00000 3.00000 −3.00000 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
\(7\) \(1\)
\(11\) \(-1\)
\(13\) \(1\)

Hecke kernels

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

\( T_{2} + 1 \)
\( T_{3} \)