Properties

Label 1089.6.a.h
Level $1089$
Weight $6$
Character orbit 1089.a
Self dual yes
Analytic conductor $174.658$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1089.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(174.657979776\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - 31q^{4} + 92q^{5} + 26q^{7} - 63q^{8} + O(q^{10}) \) \( q + q^{2} - 31q^{4} + 92q^{5} + 26q^{7} - 63q^{8} + 92q^{10} + 692q^{13} + 26q^{14} + 929q^{16} - 1442q^{17} - 2160q^{19} - 2852q^{20} + 1582q^{23} + 5339q^{25} + 692q^{26} - 806q^{28} - 5526q^{29} + 4792q^{31} + 2945q^{32} - 1442q^{34} + 2392q^{35} - 10194q^{37} - 2160q^{38} - 5796q^{40} - 10622q^{41} - 8580q^{43} + 1582q^{46} + 2362q^{47} - 16131q^{49} + 5339q^{50} - 21452q^{52} + 30804q^{53} - 1638q^{56} - 5526q^{58} - 6416q^{59} - 42096q^{61} + 4792q^{62} - 26783q^{64} + 63664q^{65} - 28444q^{67} + 44702q^{68} + 2392q^{70} - 45690q^{71} + 18374q^{73} - 10194q^{74} + 66960q^{76} + 105214q^{79} + 85468q^{80} - 10622q^{82} + 62292q^{83} - 132664q^{85} - 8580q^{86} + 72246q^{89} + 17992q^{91} - 49042q^{92} + 2362q^{94} - 198720q^{95} + 79262q^{97} - 16131q^{98} + O(q^{100}) \)

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 0 −31.0000 92.0000 0 26.0000 −63.0000 0 92.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(11\) \(-1\)

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 1089.6.a.h 1
3.b odd 2 1 363.6.a.b 1
11.b odd 2 1 99.6.a.a 1
33.d even 2 1 33.6.a.b 1
132.d odd 2 1 528.6.a.a 1
165.d even 2 1 825.6.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
33.6.a.b 1 33.d even 2 1
99.6.a.a 1 11.b odd 2 1
363.6.a.b 1 3.b odd 2 1
528.6.a.a 1 132.d odd 2 1
825.6.a.a 1 165.d even 2 1
1089.6.a.h 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 \(S_{6}^{\mathrm{new}}(\Gamma_0(1089))\):

\( T_{2} - 1 \)
\( T_{5} - 92 \)
\( T_{7} - 26 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( -92 + T \)
$7$ \( -26 + T \)
$11$ \( T \)
$13$ \( -692 + T \)
$17$ \( 1442 + T \)
$19$ \( 2160 + T \)
$23$ \( -1582 + T \)
$29$ \( 5526 + T \)
$31$ \( -4792 + T \)
$37$ \( 10194 + T \)
$41$ \( 10622 + T \)
$43$ \( 8580 + T \)
$47$ \( -2362 + T \)
$53$ \( -30804 + T \)
$59$ \( 6416 + T \)
$61$ \( 42096 + T \)
$67$ \( 28444 + T \)
$71$ \( 45690 + T \)
$73$ \( -18374 + T \)
$79$ \( -105214 + T \)
$83$ \( -62292 + T \)
$89$ \( -72246 + T \)
$97$ \( -79262 + T \)
show more
show less