Properties

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

Related objects

Downloads

Learn more

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

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

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.k 1
13.b even 2 1 7098.2.a.bc 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 1.a even 1 1 trivial
7098.2.a.bc 1 13.b even 2 1

Hecke kernels

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -1 + T \)
$5$ \( 2 + T \)
$7$ \( -1 + T \)
$11$ \( T \)
$13$ \( T \)
$17$ \( -2 + T \)
$19$ \( 4 + T \)
$23$ \( -6 + T \)
$29$ \( T \)
$31$ \( T \)
$37$ \( 2 + T \)
$41$ \( T \)
$43$ \( 4 + T \)
$47$ \( -8 + T \)
$53$ \( -4 + T \)
$59$ \( 6 + T \)
$61$ \( -12 + T \)
$67$ \( -2 + T \)
$71$ \( T \)
$73$ \( 14 + T \)
$79$ \( T \)
$83$ \( -14 + T \)
$89$ \( -4 + T \)
$97$ \( -2 + T \)
show more
show less