Properties

Label 1110.2.a.d
Level $1110$
Weight $2$
Character orbit 1110.a
Self dual yes
Analytic conductor $8.863$
Analytic rank $1$
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: \(1\)
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

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

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

\( T_{7} - 3 \)
\( T_{11} + 5 \)
\( T_{13} + 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 + T \)
$5$ \( -1 + T \)
$7$ \( -3 + T \)
$11$ \( 5 + T \)
$13$ \( 2 + T \)
$17$ \( 7 + T \)
$19$ \( 2 + T \)
$23$ \( -4 + T \)
$29$ \( 5 + T \)
$31$ \( 7 + T \)
$37$ \( -1 + T \)
$41$ \( -1 + T \)
$43$ \( -9 + T \)
$47$ \( T \)
$53$ \( -3 + T \)
$59$ \( 14 + T \)
$61$ \( 7 + T \)
$67$ \( 4 + T \)
$71$ \( -8 + T \)
$73$ \( 12 + T \)
$79$ \( -4 + T \)
$83$ \( 10 + T \)
$89$ \( 14 + T \)
$97$ \( -1 + T \)
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