Properties

Label 110.2.a.b
Level 110
Weight 2
Character orbit 110.a
Self dual yes
Analytic conductor 0.878
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 110 = 2 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 110.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.878354422234\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 3q^{7} + q^{8} - 2q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 3q^{7} + q^{8} - 2q^{9} + q^{10} + q^{11} - q^{12} - 6q^{13} + 3q^{14} - q^{15} + q^{16} - 7q^{17} - 2q^{18} + 5q^{19} + q^{20} - 3q^{21} + q^{22} - 6q^{23} - q^{24} + q^{25} - 6q^{26} + 5q^{27} + 3q^{28} + 5q^{29} - q^{30} - 3q^{31} + q^{32} - q^{33} - 7q^{34} + 3q^{35} - 2q^{36} + 3q^{37} + 5q^{38} + 6q^{39} + q^{40} + 2q^{41} - 3q^{42} + 4q^{43} + q^{44} - 2q^{45} - 6q^{46} - 2q^{47} - q^{48} + 2q^{49} + q^{50} + 7q^{51} - 6q^{52} - q^{53} + 5q^{54} + q^{55} + 3q^{56} - 5q^{57} + 5q^{58} - 10q^{59} - q^{60} + 7q^{61} - 3q^{62} - 6q^{63} + q^{64} - 6q^{65} - q^{66} + 8q^{67} - 7q^{68} + 6q^{69} + 3q^{70} + 7q^{71} - 2q^{72} + 14q^{73} + 3q^{74} - q^{75} + 5q^{76} + 3q^{77} + 6q^{78} + 10q^{79} + q^{80} + q^{81} + 2q^{82} - 6q^{83} - 3q^{84} - 7q^{85} + 4q^{86} - 5q^{87} + q^{88} - 15q^{89} - 2q^{90} - 18q^{91} - 6q^{92} + 3q^{93} - 2q^{94} + 5q^{95} - q^{96} - 12q^{97} + 2q^{98} - 2q^{99} + O(q^{100}) \)

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
1.00000 −1.00000 1.00000 1.00000 −1.00000 3.00000 1.00000 −2.00000 1.00000
\(n\): 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 110.2.a.b 1
3.b odd 2 1 990.2.a.d 1
4.b odd 2 1 880.2.a.i 1
5.b even 2 1 550.2.a.f 1
5.c odd 4 2 550.2.b.a 2
7.b odd 2 1 5390.2.a.bf 1
8.b even 2 1 3520.2.a.y 1
8.d odd 2 1 3520.2.a.h 1
11.b odd 2 1 1210.2.a.b 1
12.b even 2 1 7920.2.a.d 1
15.d odd 2 1 4950.2.a.bc 1
15.e even 4 2 4950.2.c.m 2
20.d odd 2 1 4400.2.a.l 1
20.e even 4 2 4400.2.b.i 2
44.c even 2 1 9680.2.a.x 1
55.d odd 2 1 6050.2.a.bj 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
110.2.a.b 1 1.a even 1 1 trivial
550.2.a.f 1 5.b even 2 1
550.2.b.a 2 5.c odd 4 2
880.2.a.i 1 4.b odd 2 1
990.2.a.d 1 3.b odd 2 1
1210.2.a.b 1 11.b odd 2 1
3520.2.a.h 1 8.d odd 2 1
3520.2.a.y 1 8.b even 2 1
4400.2.a.l 1 20.d odd 2 1
4400.2.b.i 2 20.e even 4 2
4950.2.a.bc 1 15.d odd 2 1
4950.2.c.m 2 15.e even 4 2
5390.2.a.bf 1 7.b odd 2 1
6050.2.a.bj 1 55.d odd 2 1
7920.2.a.d 1 12.b even 2 1
9680.2.a.x 1 44.c even 2 1

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(110))\):

\( T_{3} + 1 \)
\( T_{7} - 3 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - T \)
$3$ \( 1 + T + 3 T^{2} \)
$5$ \( 1 - T \)
$7$ \( 1 - 3 T + 7 T^{2} \)
$11$ \( 1 - T \)
$13$ \( 1 + 6 T + 13 T^{2} \)
$17$ \( 1 + 7 T + 17 T^{2} \)
$19$ \( 1 - 5 T + 19 T^{2} \)
$23$ \( 1 + 6 T + 23 T^{2} \)
$29$ \( 1 - 5 T + 29 T^{2} \)
$31$ \( 1 + 3 T + 31 T^{2} \)
$37$ \( 1 - 3 T + 37 T^{2} \)
$41$ \( 1 - 2 T + 41 T^{2} \)
$43$ \( 1 - 4 T + 43 T^{2} \)
$47$ \( 1 + 2 T + 47 T^{2} \)
$53$ \( 1 + T + 53 T^{2} \)
$59$ \( 1 + 10 T + 59 T^{2} \)
$61$ \( 1 - 7 T + 61 T^{2} \)
$67$ \( 1 - 8 T + 67 T^{2} \)
$71$ \( 1 - 7 T + 71 T^{2} \)
$73$ \( 1 - 14 T + 73 T^{2} \)
$79$ \( 1 - 10 T + 79 T^{2} \)
$83$ \( 1 + 6 T + 83 T^{2} \)
$89$ \( 1 + 15 T + 89 T^{2} \)
$97$ \( 1 + 12 T + 97 T^{2} \)
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