Properties

Label 8036.2.a.d
Level 8036
Weight 2
Character orbit 8036.a
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
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

\(f(q)\) \(=\) \( q + q^{3} - 3q^{5} - 2q^{9} + O(q^{10}) \) \( q + q^{3} - 3q^{5} - 2q^{9} + 3q^{11} - 4q^{13} - 3q^{15} - 7q^{19} + 6q^{23} + 4q^{25} - 5q^{27} + 6q^{29} - 10q^{31} + 3q^{33} + 2q^{37} - 4q^{39} - q^{41} - 4q^{43} + 6q^{45} + 12q^{47} - 6q^{53} - 9q^{55} - 7q^{57} + 6q^{59} - 13q^{61} + 12q^{65} - 4q^{67} + 6q^{69} - 9q^{71} + 14q^{73} + 4q^{75} - q^{79} + q^{81} + 12q^{83} + 6q^{87} - 12q^{89} - 10q^{93} + 21q^{95} + 2q^{97} - 6q^{99} + O(q^{100}) \)

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
0 1.00000 0 −3.00000 0 0 0 −2.00000 0
\(n\): 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
\(2\) \(-1\)
\(7\) \(1\)
\(41\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8036))\):

\( T_{3} - 1 \)
\( T_{5} + 3 \)
\( T_{11} - 3 \)