Properties

Label 7018.2.a.a
Level $7018$
Weight $2$
Character orbit 7018.a
Self dual yes
Analytic conductor $56.039$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7018 = 2 \cdot 11^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7018.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.0390121385\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 58)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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 2.00000 −1.00000 −2.00000 −1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(11\) \(-1\)
\(29\) \(-1\)

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 7018.2.a.a 1
11.b odd 2 1 58.2.a.b 1
33.d even 2 1 522.2.a.b 1
44.c even 2 1 464.2.a.e 1
55.d odd 2 1 1450.2.a.c 1
55.e even 4 2 1450.2.b.b 2
77.b even 2 1 2842.2.a.e 1
88.b odd 2 1 1856.2.a.k 1
88.g even 2 1 1856.2.a.f 1
132.d odd 2 1 4176.2.a.n 1
143.d odd 2 1 9802.2.a.a 1
319.d odd 2 1 1682.2.a.d 1
319.f even 4 2 1682.2.b.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
58.2.a.b 1 11.b odd 2 1
464.2.a.e 1 44.c even 2 1
522.2.a.b 1 33.d even 2 1
1450.2.a.c 1 55.d odd 2 1
1450.2.b.b 2 55.e even 4 2
1682.2.a.d 1 319.d odd 2 1
1682.2.b.a 2 319.f even 4 2
1856.2.a.f 1 88.g even 2 1
1856.2.a.k 1 88.b odd 2 1
2842.2.a.e 1 77.b even 2 1
4176.2.a.n 1 132.d odd 2 1
7018.2.a.a 1 1.a even 1 1 trivial
9802.2.a.a 1 143.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7018))\):

\( T_{3} + 1 \) Copy content Toggle raw display
\( T_{5} - 1 \) Copy content Toggle raw display
\( T_{7} - 2 \) Copy content Toggle raw display
\( T_{13} - 1 \) Copy content Toggle raw display

Hecke characteristic polynomials

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