Properties

Label 880.2.a.i
Level $880$
Weight $2$
Character orbit 880.a
Self dual yes
Analytic conductor $7.027$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.02683537787\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 110)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + q^{5} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} + q^{5} - 3 q^{7} - 2 q^{9} - q^{11} - 6 q^{13} + q^{15} - 7 q^{17} - 5 q^{19} - 3 q^{21} + 6 q^{23} + q^{25} - 5 q^{27} + 5 q^{29} + 3 q^{31} - q^{33} - 3 q^{35} + 3 q^{37} - 6 q^{39} + 2 q^{41} - 4 q^{43} - 2 q^{45} + 2 q^{47} + 2 q^{49} - 7 q^{51} - q^{53} - q^{55} - 5 q^{57} + 10 q^{59} + 7 q^{61} + 6 q^{63} - 6 q^{65} - 8 q^{67} + 6 q^{69} - 7 q^{71} + 14 q^{73} + q^{75} + 3 q^{77} - 10 q^{79} + q^{81} + 6 q^{83} - 7 q^{85} + 5 q^{87} - 15 q^{89} + 18 q^{91} + 3 q^{93} - 5 q^{95} - 12 q^{97} + 2 q^{99}+O(q^{100}) \) 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 1.00000 0 1.00000 0 −3.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(-1\)
\(11\) \(1\)

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 880.2.a.i 1
3.b odd 2 1 7920.2.a.d 1
4.b odd 2 1 110.2.a.b 1
5.b even 2 1 4400.2.a.l 1
5.c odd 4 2 4400.2.b.i 2
8.b even 2 1 3520.2.a.h 1
8.d odd 2 1 3520.2.a.y 1
11.b odd 2 1 9680.2.a.x 1
12.b even 2 1 990.2.a.d 1
20.d odd 2 1 550.2.a.f 1
20.e even 4 2 550.2.b.a 2
28.d even 2 1 5390.2.a.bf 1
44.c even 2 1 1210.2.a.b 1
60.h even 2 1 4950.2.a.bc 1
60.l odd 4 2 4950.2.c.m 2
220.g even 2 1 6050.2.a.bj 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
110.2.a.b 1 4.b odd 2 1
550.2.a.f 1 20.d odd 2 1
550.2.b.a 2 20.e even 4 2
880.2.a.i 1 1.a even 1 1 trivial
990.2.a.d 1 12.b even 2 1
1210.2.a.b 1 44.c even 2 1
3520.2.a.h 1 8.b even 2 1
3520.2.a.y 1 8.d odd 2 1
4400.2.a.l 1 5.b even 2 1
4400.2.b.i 2 5.c odd 4 2
4950.2.a.bc 1 60.h even 2 1
4950.2.c.m 2 60.l odd 4 2
5390.2.a.bf 1 28.d even 2 1
6050.2.a.bj 1 220.g even 2 1
7920.2.a.d 1 3.b odd 2 1
9680.2.a.x 1 11.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(880))\):

\( T_{3} - 1 \) Copy content Toggle raw display
\( T_{7} + 3 \) 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
$3$ \( T - 1 \) Copy content Toggle raw display
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T + 3 \) Copy content Toggle raw display
$11$ \( T + 1 \) Copy content Toggle raw display
$13$ \( T + 6 \) Copy content Toggle raw display
$17$ \( T + 7 \) Copy content Toggle raw display
$19$ \( T + 5 \) Copy content Toggle raw display
$23$ \( T - 6 \) Copy content Toggle raw display
$29$ \( T - 5 \) Copy content Toggle raw display
$31$ \( T - 3 \) Copy content Toggle raw display
$37$ \( T - 3 \) Copy content Toggle raw display
$41$ \( T - 2 \) Copy content Toggle raw display
$43$ \( T + 4 \) Copy content Toggle raw display
$47$ \( T - 2 \) Copy content Toggle raw display
$53$ \( T + 1 \) Copy content Toggle raw display
$59$ \( T - 10 \) Copy content Toggle raw display
$61$ \( T - 7 \) Copy content Toggle raw display
$67$ \( T + 8 \) Copy content Toggle raw display
$71$ \( T + 7 \) Copy content Toggle raw display
$73$ \( T - 14 \) Copy content Toggle raw display
$79$ \( T + 10 \) Copy content Toggle raw display
$83$ \( T - 6 \) Copy content Toggle raw display
$89$ \( T + 15 \) Copy content Toggle raw display
$97$ \( T + 12 \) Copy content Toggle raw display
show more
show less