Properties

Label 5010.2.a.h
Level 5010
Weight 2
Character orbit 5010.a
Self dual Yes
Analytic conductor 40.005
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 5010 = 2 \cdot 3 \cdot 5 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.0050514127\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 2q^{11} + q^{12} + q^{14} + q^{15} + q^{16} + 4q^{17} + q^{18} - q^{19} + q^{20} + q^{21} - 2q^{22} + 3q^{23} + q^{24} + q^{25} + q^{27} + q^{28} + 2q^{29} + q^{30} + 4q^{31} + q^{32} - 2q^{33} + 4q^{34} + q^{35} + q^{36} + 10q^{37} - q^{38} + q^{40} + 7q^{41} + q^{42} - 12q^{43} - 2q^{44} + q^{45} + 3q^{46} - 8q^{47} + q^{48} - 6q^{49} + q^{50} + 4q^{51} - 9q^{53} + q^{54} - 2q^{55} + q^{56} - q^{57} + 2q^{58} + 4q^{59} + q^{60} + 6q^{61} + 4q^{62} + q^{63} + q^{64} - 2q^{66} + 5q^{67} + 4q^{68} + 3q^{69} + q^{70} - 12q^{71} + q^{72} + 11q^{73} + 10q^{74} + q^{75} - q^{76} - 2q^{77} + 3q^{79} + q^{80} + q^{81} + 7q^{82} + 14q^{83} + q^{84} + 4q^{85} - 12q^{86} + 2q^{87} - 2q^{88} + 6q^{89} + q^{90} + 3q^{92} + 4q^{93} - 8q^{94} - q^{95} + q^{96} - 6q^{98} - 2q^{99} + O(q^{100}) \)

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 1.00000 1.00000 1.00000 1.00000 1.00000 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
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(-1\)
\(167\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5010))\):

\( T_{7} - 1 \)
\( T_{11} + 2 \)
\( T_{13} \)