Properties

Label 7220.2.a.a
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: \( 1 \)
Twist minimal: no (minimal twist has level 380)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2 q^{3} - q^{5} - 4 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{3} - q^{5} - 4 q^{7} + q^{9} - 3 q^{11} - 6 q^{13} + 2 q^{15} + 2 q^{17} + 8 q^{21} + 4 q^{23} + q^{25} + 4 q^{27} - q^{29} + 5 q^{31} + 6 q^{33} + 4 q^{35} + 4 q^{37} + 12 q^{39} - 2 q^{41} - q^{45} + 6 q^{47} + 9 q^{49} - 4 q^{51} + 6 q^{53} + 3 q^{55} + q^{59} - 7 q^{61} - 4 q^{63} + 6 q^{65} + 14 q^{67} - 8 q^{69} - 15 q^{71} + 12 q^{73} - 2 q^{75} + 12 q^{77} + q^{79} - 11 q^{81} + 16 q^{83} - 2 q^{85} + 2 q^{87} - 17 q^{89} + 24 q^{91} - 10 q^{93} - 12 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −4.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)
\(19\) \(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 7220.2.a.a 1
19.b odd 2 1 7220.2.a.e 1
19.d odd 6 2 380.2.i.a 2
57.f even 6 2 3420.2.t.b 2
76.f even 6 2 1520.2.q.g 2
95.h odd 6 2 1900.2.i.b 2
95.l even 12 4 1900.2.s.b 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
380.2.i.a 2 19.d odd 6 2
1520.2.q.g 2 76.f even 6 2
1900.2.i.b 2 95.h odd 6 2
1900.2.s.b 4 95.l even 12 4
3420.2.t.b 2 57.f even 6 2
7220.2.a.a 1 1.a even 1 1 trivial
7220.2.a.e 1 19.b odd 2 1

Hecke kernels

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

\( T_{3} + 2 \) Copy content Toggle raw display
\( T_{7} + 4 \) Copy content Toggle raw display
\( T_{13} + 6 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T + 2 \) Copy content Toggle raw display
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T + 4 \) Copy content Toggle raw display
$11$ \( T + 3 \) Copy content Toggle raw display
$13$ \( T + 6 \) Copy content Toggle raw display
$17$ \( T - 2 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T - 4 \) Copy content Toggle raw display
$29$ \( T + 1 \) Copy content Toggle raw display
$31$ \( T - 5 \) Copy content Toggle raw display
$37$ \( T - 4 \) Copy content Toggle raw display
$41$ \( T + 2 \) Copy content Toggle raw display
$43$ \( T \) Copy content Toggle raw display
$47$ \( T - 6 \) Copy content Toggle raw display
$53$ \( T - 6 \) Copy content Toggle raw display
$59$ \( T - 1 \) Copy content Toggle raw display
$61$ \( T + 7 \) Copy content Toggle raw display
$67$ \( T - 14 \) Copy content Toggle raw display
$71$ \( T + 15 \) Copy content Toggle raw display
$73$ \( T - 12 \) Copy content Toggle raw display
$79$ \( T - 1 \) Copy content Toggle raw display
$83$ \( T - 16 \) Copy content Toggle raw display
$89$ \( T + 17 \) Copy content Toggle raw display
$97$ \( T + 12 \) Copy content Toggle raw display
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