Properties

Label 4010.2.a.a
Level 4010
Weight 2
Character orbit 4010.a
Self dual Yes
Analytic conductor 32.020
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
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

\(f(q)\) \(=\) \( q - q^{2} - 2q^{3} + q^{4} + q^{5} + 2q^{6} - 4q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - 2q^{3} + q^{4} + q^{5} + 2q^{6} - 4q^{7} - q^{8} + q^{9} - q^{10} + 3q^{11} - 2q^{12} + 5q^{13} + 4q^{14} - 2q^{15} + q^{16} - q^{18} + 8q^{19} + q^{20} + 8q^{21} - 3q^{22} + 2q^{24} + q^{25} - 5q^{26} + 4q^{27} - 4q^{28} + 2q^{30} + 5q^{31} - q^{32} - 6q^{33} - 4q^{35} + q^{36} - 10q^{37} - 8q^{38} - 10q^{39} - q^{40} - 9q^{41} - 8q^{42} + 5q^{43} + 3q^{44} + q^{45} - 2q^{48} + 9q^{49} - q^{50} + 5q^{52} - 9q^{53} - 4q^{54} + 3q^{55} + 4q^{56} - 16q^{57} - 2q^{60} - q^{61} - 5q^{62} - 4q^{63} + q^{64} + 5q^{65} + 6q^{66} - 4q^{67} + 4q^{70} - 3q^{71} - q^{72} - 7q^{73} + 10q^{74} - 2q^{75} + 8q^{76} - 12q^{77} + 10q^{78} - q^{79} + q^{80} - 11q^{81} + 9q^{82} + 3q^{83} + 8q^{84} - 5q^{86} - 3q^{88} + 15q^{89} - q^{90} - 20q^{91} - 10q^{93} + 8q^{95} + 2q^{96} + 14q^{97} - 9q^{98} + 3q^{99} + O(q^{100}) \)

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 −2.00000 1.00000 1.00000 2.00000 −4.00000 −1.00000 1.00000 −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
\(2\) \(1\)
\(5\) \(-1\)
\(401\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4010))\):

\( T_{3} + 2 \)
\( T_{7} + 4 \)
\( T_{11} - 3 \)