Properties

Label 8036.2.a.e
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

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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

\(f(q)\) \(=\) \( q + q^{3} + q^{5} - 2q^{9} + O(q^{10}) \) \( q + q^{3} + q^{5} - 2q^{9} - 5q^{11} + 2q^{13} + q^{15} + 3q^{17} + 3q^{19} - q^{23} - 4q^{25} - 5q^{27} - 10q^{29} + 11q^{31} - 5q^{33} + 7q^{37} + 2q^{39} + q^{41} + 8q^{43} - 2q^{45} + 7q^{47} + 3q^{51} - 11q^{53} - 5q^{55} + 3q^{57} + 7q^{59} + q^{61} + 2q^{65} + 7q^{67} - q^{69} - 12q^{71} + 5q^{73} - 4q^{75} + 9q^{79} + q^{81} + 3q^{85} - 10q^{87} + 3q^{89} + 11q^{93} + 3q^{95} - 2q^{97} + 10q^{99} + O(q^{100}) \)

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 1.00000 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8036))\):

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