Properties

Label 1110.4.a.b
Level $1110$
Weight $4$
Character orbit 1110.a
Self dual yes
Analytic conductor $65.492$
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: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1110.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(65.4921201064\)
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

\(f(q)\) \(=\) \( q + 2q^{2} - 3q^{3} + 4q^{4} - 5q^{5} - 6q^{6} + 10q^{7} + 8q^{8} + 9q^{9} + O(q^{10}) \) \( q + 2q^{2} - 3q^{3} + 4q^{4} - 5q^{5} - 6q^{6} + 10q^{7} + 8q^{8} + 9q^{9} - 10q^{10} + 44q^{11} - 12q^{12} + 59q^{13} + 20q^{14} + 15q^{15} + 16q^{16} - 46q^{17} + 18q^{18} - 34q^{19} - 20q^{20} - 30q^{21} + 88q^{22} + 6q^{23} - 24q^{24} + 25q^{25} + 118q^{26} - 27q^{27} + 40q^{28} + 7q^{29} + 30q^{30} - 182q^{31} + 32q^{32} - 132q^{33} - 92q^{34} - 50q^{35} + 36q^{36} + 37q^{37} - 68q^{38} - 177q^{39} - 40q^{40} + 360q^{41} - 60q^{42} + 101q^{43} + 176q^{44} - 45q^{45} + 12q^{46} - 35q^{47} - 48q^{48} - 243q^{49} + 50q^{50} + 138q^{51} + 236q^{52} - 507q^{53} - 54q^{54} - 220q^{55} + 80q^{56} + 102q^{57} + 14q^{58} + 821q^{59} + 60q^{60} + 70q^{61} - 364q^{62} + 90q^{63} + 64q^{64} - 295q^{65} - 264q^{66} + 612q^{67} - 184q^{68} - 18q^{69} - 100q^{70} + 88q^{71} + 72q^{72} + 622q^{73} + 74q^{74} - 75q^{75} - 136q^{76} + 440q^{77} - 354q^{78} + 8q^{79} - 80q^{80} + 81q^{81} + 720q^{82} + 1223q^{83} - 120q^{84} + 230q^{85} + 202q^{86} - 21q^{87} + 352q^{88} + 345q^{89} - 90q^{90} + 590q^{91} + 24q^{92} + 546q^{93} - 70q^{94} + 170q^{95} - 96q^{96} + 870q^{97} - 486q^{98} + 396q^{99} + O(q^{100}) \)

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
2.00000 −3.00000 4.00000 −5.00000 −6.00000 10.0000 8.00000 9.00000 −10.0000
\(n\): 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 1110.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1110.4.a.b 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7} - 10 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1110))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( 3 + T \)
$5$ \( 5 + T \)
$7$ \( -10 + T \)
$11$ \( -44 + T \)
$13$ \( -59 + T \)
$17$ \( 46 + T \)
$19$ \( 34 + T \)
$23$ \( -6 + T \)
$29$ \( -7 + T \)
$31$ \( 182 + T \)
$37$ \( -37 + T \)
$41$ \( -360 + T \)
$43$ \( -101 + T \)
$47$ \( 35 + T \)
$53$ \( 507 + T \)
$59$ \( -821 + T \)
$61$ \( -70 + T \)
$67$ \( -612 + T \)
$71$ \( -88 + T \)
$73$ \( -622 + T \)
$79$ \( -8 + T \)
$83$ \( -1223 + T \)
$89$ \( -345 + T \)
$97$ \( -870 + T \)
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