Properties

Label 1100.2.a.e
Level 1100
Weight 2
Character orbit 1100.a
Self dual yes
Analytic conductor 8.784
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1100.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.78354422234\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 220)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{3} + 4q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{3} + 4q^{7} + q^{9} - q^{11} + 4q^{13} - 4q^{19} + 8q^{21} + 6q^{23} - 4q^{27} - 6q^{29} + 8q^{31} - 2q^{33} - 2q^{37} + 8q^{39} + 6q^{41} - 8q^{43} - 6q^{47} + 9q^{49} + 6q^{53} - 8q^{57} - 12q^{59} + 2q^{61} + 4q^{63} + 10q^{67} + 12q^{69} - 12q^{71} + 16q^{73} - 4q^{77} + 8q^{79} - 11q^{81} - 12q^{87} + 6q^{89} + 16q^{91} + 16q^{93} - 14q^{97} - q^{99} + O(q^{100}) \)

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 2.00000 0 0 0 4.00000 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.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1100.2.a.e 1
3.b odd 2 1 9900.2.a.bd 1
4.b odd 2 1 4400.2.a.e 1
5.b even 2 1 220.2.a.a 1
5.c odd 4 2 1100.2.b.a 2
15.d odd 2 1 1980.2.a.a 1
15.e even 4 2 9900.2.c.m 2
20.d odd 2 1 880.2.a.j 1
20.e even 4 2 4400.2.b.f 2
40.e odd 2 1 3520.2.a.d 1
40.f even 2 1 3520.2.a.bd 1
55.d odd 2 1 2420.2.a.b 1
60.h even 2 1 7920.2.a.o 1
220.g even 2 1 9680.2.a.bb 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
220.2.a.a 1 5.b even 2 1
880.2.a.j 1 20.d odd 2 1
1100.2.a.e 1 1.a even 1 1 trivial
1100.2.b.a 2 5.c odd 4 2
1980.2.a.a 1 15.d odd 2 1
2420.2.a.b 1 55.d odd 2 1
3520.2.a.d 1 40.e odd 2 1
3520.2.a.bd 1 40.f even 2 1
4400.2.a.e 1 4.b odd 2 1
4400.2.b.f 2 20.e even 4 2
7920.2.a.o 1 60.h even 2 1
9680.2.a.bb 1 220.g even 2 1
9900.2.a.bd 1 3.b odd 2 1
9900.2.c.m 2 15.e even 4 2

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1100))\):

\( T_{3} - 2 \)
\( T_{7} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 2 T + 3 T^{2} \)
$5$ 1
$7$ \( 1 - 4 T + 7 T^{2} \)
$11$ \( 1 + T \)
$13$ \( 1 - 4 T + 13 T^{2} \)
$17$ \( 1 + 17 T^{2} \)
$19$ \( 1 + 4 T + 19 T^{2} \)
$23$ \( 1 - 6 T + 23 T^{2} \)
$29$ \( 1 + 6 T + 29 T^{2} \)
$31$ \( 1 - 8 T + 31 T^{2} \)
$37$ \( 1 + 2 T + 37 T^{2} \)
$41$ \( 1 - 6 T + 41 T^{2} \)
$43$ \( 1 + 8 T + 43 T^{2} \)
$47$ \( 1 + 6 T + 47 T^{2} \)
$53$ \( 1 - 6 T + 53 T^{2} \)
$59$ \( 1 + 12 T + 59 T^{2} \)
$61$ \( 1 - 2 T + 61 T^{2} \)
$67$ \( 1 - 10 T + 67 T^{2} \)
$71$ \( 1 + 12 T + 71 T^{2} \)
$73$ \( 1 - 16 T + 73 T^{2} \)
$79$ \( 1 - 8 T + 79 T^{2} \)
$83$ \( 1 + 83 T^{2} \)
$89$ \( 1 - 6 T + 89 T^{2} \)
$97$ \( 1 + 14 T + 97 T^{2} \)
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