Properties

Label 1008.2.a.b
Level 1008
Weight 2
Character orbit 1008.a
Self dual yes
Analytic conductor 8.049
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 168)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{5} - q^{7} + O(q^{10}) \) \( q - 2q^{5} - q^{7} + 6q^{13} + 2q^{17} - 4q^{19} - 4q^{23} - q^{25} + 10q^{29} + 8q^{31} + 2q^{35} + 6q^{37} + 2q^{41} + 4q^{43} + 8q^{47} + q^{49} + 10q^{53} + 12q^{59} - 2q^{61} - 12q^{65} - 12q^{67} - 12q^{71} - 14q^{73} + 8q^{79} + 12q^{83} - 4q^{85} + 2q^{89} - 6q^{91} + 8q^{95} + 10q^{97} + O(q^{100}) \)

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 −2.00000 0 −1.00000 0 0 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 1008.2.a.b 1
3.b odd 2 1 336.2.a.e 1
4.b odd 2 1 504.2.a.e 1
7.b odd 2 1 7056.2.a.bq 1
8.b even 2 1 4032.2.a.bc 1
8.d odd 2 1 4032.2.a.bh 1
12.b even 2 1 168.2.a.a 1
15.d odd 2 1 8400.2.a.y 1
21.c even 2 1 2352.2.a.c 1
21.g even 6 2 2352.2.q.w 2
21.h odd 6 2 2352.2.q.d 2
24.f even 2 1 1344.2.a.m 1
24.h odd 2 1 1344.2.a.b 1
28.d even 2 1 3528.2.a.v 1
28.f even 6 2 3528.2.s.g 2
28.g odd 6 2 3528.2.s.w 2
48.i odd 4 2 5376.2.c.bb 2
48.k even 4 2 5376.2.c.d 2
60.h even 2 1 4200.2.a.t 1
60.l odd 4 2 4200.2.t.j 2
84.h odd 2 1 1176.2.a.f 1
84.j odd 6 2 1176.2.q.d 2
84.n even 6 2 1176.2.q.f 2
168.e odd 2 1 9408.2.a.be 1
168.i even 2 1 9408.2.a.da 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
168.2.a.a 1 12.b even 2 1
336.2.a.e 1 3.b odd 2 1
504.2.a.e 1 4.b odd 2 1
1008.2.a.b 1 1.a even 1 1 trivial
1176.2.a.f 1 84.h odd 2 1
1176.2.q.d 2 84.j odd 6 2
1176.2.q.f 2 84.n even 6 2
1344.2.a.b 1 24.h odd 2 1
1344.2.a.m 1 24.f even 2 1
2352.2.a.c 1 21.c even 2 1
2352.2.q.d 2 21.h odd 6 2
2352.2.q.w 2 21.g even 6 2
3528.2.a.v 1 28.d even 2 1
3528.2.s.g 2 28.f even 6 2
3528.2.s.w 2 28.g odd 6 2
4032.2.a.bc 1 8.b even 2 1
4032.2.a.bh 1 8.d odd 2 1
4200.2.a.t 1 60.h even 2 1
4200.2.t.j 2 60.l odd 4 2
5376.2.c.d 2 48.k even 4 2
5376.2.c.bb 2 48.i odd 4 2
7056.2.a.bq 1 7.b odd 2 1
8400.2.a.y 1 15.d odd 2 1
9408.2.a.be 1 168.e odd 2 1
9408.2.a.da 1 168.i even 2 1

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\):

\( T_{5} + 2 \)
\( T_{11} \)
\( T_{13} - 6 \)