Properties

Label 7098.2.a.u
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + 2q^{10} - q^{12} - q^{14} - 2q^{15} + q^{16} + q^{17} + q^{18} - 6q^{19} + 2q^{20} + q^{21} + 3q^{23} - q^{24} - q^{25} - q^{27} - q^{28} + 6q^{29} - 2q^{30} - 5q^{31} + q^{32} + q^{34} - 2q^{35} + q^{36} + 2q^{37} - 6q^{38} + 2q^{40} + 10q^{41} + q^{42} + 3q^{43} + 2q^{45} + 3q^{46} - 6q^{47} - q^{48} + q^{49} - q^{50} - q^{51} + 7q^{53} - q^{54} - q^{56} + 6q^{57} + 6q^{58} + 7q^{59} - 2q^{60} + 11q^{61} - 5q^{62} - q^{63} + q^{64} + 13q^{67} + q^{68} - 3q^{69} - 2q^{70} + 3q^{71} + q^{72} - 12q^{73} + 2q^{74} + q^{75} - 6q^{76} - 4q^{79} + 2q^{80} + q^{81} + 10q^{82} + 15q^{83} + q^{84} + 2q^{85} + 3q^{86} - 6q^{87} + 11q^{89} + 2q^{90} + 3q^{92} + 5q^{93} - 6q^{94} - 12q^{95} - q^{96} - 12q^{97} + q^{98} + O(q^{100}) \)

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 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.u 1
13.b even 2 1 7098.2.a.c 1
13.e even 6 2 546.2.l.f 2
39.h odd 6 2 1638.2.r.j 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
546.2.l.f 2 13.e even 6 2
1638.2.r.j 2 39.h odd 6 2
7098.2.a.c 1 13.b even 2 1
7098.2.a.u 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7098))\):

\( T_{5} - 2 \)
\( T_{11} \)
\( T_{17} - 1 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( 1 + T \)
$5$ \( -2 + T \)
$7$ \( 1 + T \)
$11$ \( T \)
$13$ \( T \)
$17$ \( -1 + T \)
$19$ \( 6 + T \)
$23$ \( -3 + T \)
$29$ \( -6 + T \)
$31$ \( 5 + T \)
$37$ \( -2 + T \)
$41$ \( -10 + T \)
$43$ \( -3 + T \)
$47$ \( 6 + T \)
$53$ \( -7 + T \)
$59$ \( -7 + T \)
$61$ \( -11 + T \)
$67$ \( -13 + T \)
$71$ \( -3 + T \)
$73$ \( 12 + T \)
$79$ \( 4 + T \)
$83$ \( -15 + T \)
$89$ \( -11 + T \)
$97$ \( 12 + T \)
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