Properties

Label 4005.2.a.d
Level 4005
Weight 2
Character orbit 4005.a
Self dual Yes
Analytic conductor 31.980
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{4} - q^{5} - 3q^{8} + O(q^{10}) \) \( q + q^{2} - q^{4} - q^{5} - 3q^{8} - q^{10} - 4q^{11} - 6q^{13} - q^{16} + 6q^{17} + 8q^{19} + q^{20} - 4q^{22} - 8q^{23} + q^{25} - 6q^{26} - 6q^{29} - 4q^{31} + 5q^{32} + 6q^{34} + 2q^{37} + 8q^{38} + 3q^{40} + 6q^{41} + 4q^{43} + 4q^{44} - 8q^{46} - 7q^{49} + q^{50} + 6q^{52} + 2q^{53} + 4q^{55} - 6q^{58} + 14q^{61} - 4q^{62} + 7q^{64} + 6q^{65} + 12q^{67} - 6q^{68} - 6q^{73} + 2q^{74} - 8q^{76} + 16q^{79} + q^{80} + 6q^{82} - 12q^{83} - 6q^{85} + 4q^{86} + 12q^{88} - q^{89} + 8q^{92} - 8q^{95} - 6q^{97} - 7q^{98} + O(q^{100}) \)

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 −1.00000 0 0 −3.00000 0 −1.00000
\(n\): 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
\(3\) \(-1\)
\(5\) \(1\)
\(89\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4005))\):

\( T_{2} - 1 \)
\( T_{7} \)
\( T_{11} + 4 \)