Properties

Label 7220.2.a.f
Level 7220
Weight 2
Character orbit 7220.a
Self dual Yes
Analytic conductor 57.652
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 7220 = 2^{2} \cdot 5 \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 7220.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(57.6519902594\)
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

\(f(q)\) \(=\) \( q + 2q^{3} - q^{5} + 2q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{3} - q^{5} + 2q^{7} + q^{9} - 2q^{13} - 2q^{15} - 6q^{17} + 4q^{21} + 6q^{23} + q^{25} - 4q^{27} - 6q^{29} + 4q^{31} - 2q^{35} - 2q^{37} - 4q^{39} - 6q^{41} - 10q^{43} - q^{45} - 6q^{47} - 3q^{49} - 12q^{51} + 6q^{53} - 12q^{59} + 2q^{61} + 2q^{63} + 2q^{65} - 2q^{67} + 12q^{69} + 12q^{71} + 2q^{73} + 2q^{75} - 8q^{79} - 11q^{81} + 6q^{83} + 6q^{85} - 12q^{87} + 6q^{89} - 4q^{91} + 8q^{93} - 2q^{97} + O(q^{100}) \)

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 2.00000 0 −1.00000 0 2.00000 0 1.00000 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
\(2\) \(-1\)
\(5\) \(1\)
\(19\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7220))\):

\( T_{3} - 2 \)
\( T_{7} - 2 \)
\( T_{13} + 2 \)