Properties

Label 1110.2.a.e
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

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

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 −1.00000 −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.e 1
3.b odd 2 1 3330.2.a.u 1
4.b odd 2 1 8880.2.a.f 1
5.b even 2 1 5550.2.a.ba 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1110.2.a.e 1 1.a even 1 1 trivial
3330.2.a.u 1 3.b odd 2 1
5550.2.a.ba 1 5.b even 2 1
8880.2.a.f 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1110))\):

\( T_{7} + 1 \)
\( T_{11} - 3 \)
\( T_{13} + 7 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -1 + T \)
$5$ \( 1 + T \)
$7$ \( 1 + T \)
$11$ \( -3 + T \)
$13$ \( 7 + T \)
$17$ \( 3 + T \)
$19$ \( 1 + T \)
$23$ \( 3 + T \)
$29$ \( -6 + T \)
$31$ \( 10 + T \)
$37$ \( -1 + T \)
$41$ \( T \)
$43$ \( 4 + T \)
$47$ \( 12 + T \)
$53$ \( -9 + T \)
$59$ \( -6 + T \)
$61$ \( 10 + T \)
$67$ \( 10 + T \)
$71$ \( 6 + T \)
$73$ \( -11 + T \)
$79$ \( -8 + T \)
$83$ \( -9 + T \)
$89$ \( 9 + T \)
$97$ \( 16 + T \)
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