Properties

Label 7098.2.a.bc
Level $7098$
Weight $2$
Character orbit 7098.a
Self dual yes
Analytic conductor $56.678$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7098.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.6778153547\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + 2 q^{5} + q^{6} - q^{7} + q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{3} + q^{4} + 2 q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + 2 q^{10} + q^{12} - q^{14} + 2 q^{15} + q^{16} + 2 q^{17} + q^{18} + 4 q^{19} + 2 q^{20} - q^{21} + 6 q^{23} + q^{24} - q^{25} + q^{27} - q^{28} + 2 q^{30} + q^{32} + 2 q^{34} - 2 q^{35} + q^{36} + 2 q^{37} + 4 q^{38} + 2 q^{40} - q^{42} - 4 q^{43} + 2 q^{45} + 6 q^{46} - 8 q^{47} + q^{48} + q^{49} - q^{50} + 2 q^{51} + 4 q^{53} + q^{54} - q^{56} + 4 q^{57} + 6 q^{59} + 2 q^{60} + 12 q^{61} - q^{63} + q^{64} - 2 q^{67} + 2 q^{68} + 6 q^{69} - 2 q^{70} + q^{72} + 14 q^{73} + 2 q^{74} - q^{75} + 4 q^{76} + 2 q^{80} + q^{81} - 14 q^{83} - q^{84} + 4 q^{85} - 4 q^{86} - 4 q^{89} + 2 q^{90} + 6 q^{92} - 8 q^{94} + 8 q^{95} + q^{96} - 2 q^{97} + q^{98}+O(q^{100}) \) 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 2.00000 1.00000 −1.00000 1.00000 1.00000 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(7\) \(1\)
\(13\) \(-1\)

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 7098.2.a.bc 1
13.b even 2 1 7098.2.a.k 1
13.d odd 4 2 546.2.c.b 2
39.f even 4 2 1638.2.c.b 2
52.f even 4 2 4368.2.h.f 2
91.i even 4 2 3822.2.c.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
546.2.c.b 2 13.d odd 4 2
1638.2.c.b 2 39.f even 4 2
3822.2.c.c 2 91.i even 4 2
4368.2.h.f 2 52.f even 4 2
7098.2.a.k 1 13.b even 2 1
7098.2.a.bc 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7098))\):

\( T_{5} - 2 \) Copy content Toggle raw display
\( T_{11} \) Copy content Toggle raw display
\( T_{17} - 2 \) 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
$5$ \( T - 2 \) Copy content Toggle raw display
$7$ \( T + 1 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T - 2 \) Copy content Toggle raw display
$19$ \( T - 4 \) Copy content Toggle raw display
$23$ \( T - 6 \) Copy content Toggle raw display
$29$ \( T \) Copy content Toggle raw display
$31$ \( T \) Copy content Toggle raw display
$37$ \( T - 2 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T + 4 \) Copy content Toggle raw display
$47$ \( T + 8 \) Copy content Toggle raw display
$53$ \( T - 4 \) Copy content Toggle raw display
$59$ \( T - 6 \) Copy content Toggle raw display
$61$ \( T - 12 \) Copy content Toggle raw display
$67$ \( T + 2 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T - 14 \) Copy content Toggle raw display
$79$ \( T \) Copy content Toggle raw display
$83$ \( T + 14 \) Copy content Toggle raw display
$89$ \( T + 4 \) Copy content Toggle raw display
$97$ \( T + 2 \) Copy content Toggle raw display
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