Properties

Label 6760.2.a.i
Level 6760
Weight 2
Character orbit 6760.a
Self dual yes
Analytic conductor 53.979
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6760 = 2^{3} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6760.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(53.9788717664\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{5} + 4q^{7} - 3q^{9} + O(q^{10}) \) \( q - q^{5} + 4q^{7} - 3q^{9} - 4q^{11} + 2q^{17} - 4q^{19} + 4q^{23} + q^{25} - 2q^{29} + 8q^{31} - 4q^{35} - 6q^{37} + 6q^{41} - 8q^{43} + 3q^{45} - 4q^{47} + 9q^{49} + 6q^{53} + 4q^{55} + 4q^{59} - 2q^{61} - 12q^{63} - 8q^{67} + 6q^{73} - 16q^{77} + 9q^{81} + 16q^{83} - 2q^{85} + 6q^{89} + 4q^{95} + 14q^{97} + 12q^{99} + O(q^{100}) \)

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
0 0 0 −1.00000 0 4.00000 0 −3.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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 6760.2.a.i 1
13.b even 2 1 40.2.a.a 1
39.d odd 2 1 360.2.a.a 1
52.b odd 2 1 80.2.a.a 1
65.d even 2 1 200.2.a.c 1
65.h odd 4 2 200.2.c.b 2
91.b odd 2 1 1960.2.a.g 1
91.r even 6 2 1960.2.q.h 2
91.s odd 6 2 1960.2.q.i 2
104.e even 2 1 320.2.a.c 1
104.h odd 2 1 320.2.a.d 1
117.n odd 6 2 3240.2.q.x 2
117.t even 6 2 3240.2.q.k 2
143.d odd 2 1 4840.2.a.f 1
156.h even 2 1 720.2.a.e 1
195.e odd 2 1 1800.2.a.v 1
195.s even 4 2 1800.2.f.a 2
208.o odd 4 2 1280.2.d.a 2
208.p even 4 2 1280.2.d.j 2
260.g odd 2 1 400.2.a.e 1
260.p even 4 2 400.2.c.d 2
312.b odd 2 1 2880.2.a.t 1
312.h even 2 1 2880.2.a.bg 1
364.h even 2 1 3920.2.a.s 1
455.h odd 2 1 9800.2.a.x 1
520.b odd 2 1 1600.2.a.k 1
520.p even 2 1 1600.2.a.o 1
520.bc even 4 2 1600.2.c.m 2
520.bg odd 4 2 1600.2.c.k 2
572.b even 2 1 9680.2.a.q 1
780.d even 2 1 3600.2.a.h 1
780.w odd 4 2 3600.2.f.t 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
40.2.a.a 1 13.b even 2 1
80.2.a.a 1 52.b odd 2 1
200.2.a.c 1 65.d even 2 1
200.2.c.b 2 65.h odd 4 2
320.2.a.c 1 104.e even 2 1
320.2.a.d 1 104.h odd 2 1
360.2.a.a 1 39.d odd 2 1
400.2.a.e 1 260.g odd 2 1
400.2.c.d 2 260.p even 4 2
720.2.a.e 1 156.h even 2 1
1280.2.d.a 2 208.o odd 4 2
1280.2.d.j 2 208.p even 4 2
1600.2.a.k 1 520.b odd 2 1
1600.2.a.o 1 520.p even 2 1
1600.2.c.k 2 520.bg odd 4 2
1600.2.c.m 2 520.bc even 4 2
1800.2.a.v 1 195.e odd 2 1
1800.2.f.a 2 195.s even 4 2
1960.2.a.g 1 91.b odd 2 1
1960.2.q.h 2 91.r even 6 2
1960.2.q.i 2 91.s odd 6 2
2880.2.a.t 1 312.b odd 2 1
2880.2.a.bg 1 312.h even 2 1
3240.2.q.k 2 117.t even 6 2
3240.2.q.x 2 117.n odd 6 2
3600.2.a.h 1 780.d even 2 1
3600.2.f.t 2 780.w odd 4 2
3920.2.a.s 1 364.h even 2 1
4840.2.a.f 1 143.d odd 2 1
6760.2.a.i 1 1.a even 1 1 trivial
9680.2.a.q 1 572.b even 2 1
9800.2.a.x 1 455.h odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)
\(13\) \(1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6760))\):

\( T_{3} \)
\( T_{7} - 4 \)
\( T_{11} + 4 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( \)
$3$ \( 1 + 3 T^{2} \)
$5$ \( 1 + T \)
$7$ \( 1 - 4 T + 7 T^{2} \)
$11$ \( 1 + 4 T + 11 T^{2} \)
$13$ \( \)
$17$ \( 1 - 2 T + 17 T^{2} \)
$19$ \( 1 + 4 T + 19 T^{2} \)
$23$ \( 1 - 4 T + 23 T^{2} \)
$29$ \( 1 + 2 T + 29 T^{2} \)
$31$ \( 1 - 8 T + 31 T^{2} \)
$37$ \( 1 + 6 T + 37 T^{2} \)
$41$ \( 1 - 6 T + 41 T^{2} \)
$43$ \( 1 + 8 T + 43 T^{2} \)
$47$ \( 1 + 4 T + 47 T^{2} \)
$53$ \( 1 - 6 T + 53 T^{2} \)
$59$ \( 1 - 4 T + 59 T^{2} \)
$61$ \( 1 + 2 T + 61 T^{2} \)
$67$ \( 1 + 8 T + 67 T^{2} \)
$71$ \( 1 + 71 T^{2} \)
$73$ \( 1 - 6 T + 73 T^{2} \)
$79$ \( 1 + 79 T^{2} \)
$83$ \( 1 - 16 T + 83 T^{2} \)
$89$ \( 1 - 6 T + 89 T^{2} \)
$97$ \( 1 - 14 T + 97 T^{2} \)
show more
show less