Properties

Label 1110.2.a.k
Level $1110$
Weight $2$
Character orbit 1110.a
Self dual yes
Analytic conductor $8.863$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.86339462436\)
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

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

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(5\) \(-1\)
\(37\) \(-1\)

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 1110.2.a.k 1
3.b odd 2 1 3330.2.a.c 1
4.b odd 2 1 8880.2.a.ba 1
5.b even 2 1 5550.2.a.r 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1110.2.a.k 1 1.a even 1 1 trivial
3330.2.a.c 1 3.b odd 2 1
5550.2.a.r 1 5.b even 2 1
8880.2.a.ba 1 4.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1110))\):

\( T_{7} \)
\( T_{11} - 4 \)
\( T_{13} + 2 \)