Properties

Label 4017.2.a.b
Level 4017
Weight 2
Character orbit 4017.a
Self dual Yes
Analytic conductor 32.076
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} - q^{4} + 2q^{5} - q^{6} - 2q^{7} + 3q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} - q^{4} + 2q^{5} - q^{6} - 2q^{7} + 3q^{8} + q^{9} - 2q^{10} + 4q^{11} - q^{12} - q^{13} + 2q^{14} + 2q^{15} - q^{16} - 6q^{17} - q^{18} - 2q^{19} - 2q^{20} - 2q^{21} - 4q^{22} - 2q^{23} + 3q^{24} - q^{25} + q^{26} + q^{27} + 2q^{28} - 2q^{29} - 2q^{30} + 8q^{31} - 5q^{32} + 4q^{33} + 6q^{34} - 4q^{35} - q^{36} - 4q^{37} + 2q^{38} - q^{39} + 6q^{40} - 10q^{41} + 2q^{42} + 4q^{43} - 4q^{44} + 2q^{45} + 2q^{46} - 8q^{47} - q^{48} - 3q^{49} + q^{50} - 6q^{51} + q^{52} + 4q^{53} - q^{54} + 8q^{55} - 6q^{56} - 2q^{57} + 2q^{58} - 8q^{59} - 2q^{60} - 2q^{61} - 8q^{62} - 2q^{63} + 7q^{64} - 2q^{65} - 4q^{66} - 4q^{67} + 6q^{68} - 2q^{69} + 4q^{70} - 8q^{71} + 3q^{72} + 4q^{74} - q^{75} + 2q^{76} - 8q^{77} + q^{78} - 2q^{80} + q^{81} + 10q^{82} + 4q^{83} + 2q^{84} - 12q^{85} - 4q^{86} - 2q^{87} + 12q^{88} + 6q^{89} - 2q^{90} + 2q^{91} + 2q^{92} + 8q^{93} + 8q^{94} - 4q^{95} - 5q^{96} + 2q^{97} + 3q^{98} + 4q^{99} + O(q^{100}) \)

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 2.00000 −1.00000 −2.00000 3.00000 1.00000 −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
\(3\) \(-1\)
\(13\) \(1\)
\(103\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4017))\):

\( T_{2} + 1 \)
\( T_{23} + 2 \)