Properties

Label 567.1.l.b
Level $567$
Weight $1$
Character orbit 567.l
Analytic conductor $0.283$
Analytic rank $0$
Dimension $2$
Projective image $D_{2}$
CM/RM discs -3, -7, 21
Inner twists $8$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 567.l (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.282969862163\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Projective image \(D_{2}\)
Projective field Galois closure of \(\Q(\sqrt{-3}, \sqrt{-7})\)
Artin image $C_3\times D_4$
Artin field Galois closure of 12.6.136738899331083.1

$q$-expansion

The \(q\)-expansion and trace form are shown below.

\(f(q)\) \(=\) \( q + \zeta_{6} q^{4} -\zeta_{6}^{2} q^{7} +O(q^{10})\) \( q + \zeta_{6} q^{4} -\zeta_{6}^{2} q^{7} + \zeta_{6}^{2} q^{16} + \zeta_{6}^{2} q^{25} + q^{28} -2 q^{37} -2 \zeta_{6}^{2} q^{43} -\zeta_{6} q^{49} - q^{64} -2 \zeta_{6} q^{67} + 2 \zeta_{6}^{2} q^{79} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{4} + q^{7} + O(q^{10}) \) \( 2q + q^{4} + q^{7} - q^{16} - q^{25} + 2q^{28} - 4q^{37} + 2q^{43} - q^{49} - 2q^{64} - 2q^{67} - 2q^{79} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(-1\) \(-\zeta_{6}\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
55.1
0.500000 + 0.866025i
0.500000 0.866025i
0 0 0.500000 + 0.866025i 0 0 0.500000 0.866025i 0 0 0
433.1 0 0 0.500000 0.866025i 0 0 0.500000 + 0.866025i 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 CM by \(\Q(\sqrt{-3}) \)
7.b odd 2 1 CM by \(\Q(\sqrt{-7}) \)
21.c even 2 1 RM by \(\Q(\sqrt{21}) \)
9.c even 3 1 inner
9.d odd 6 1 inner
63.l odd 6 1 inner
63.o even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 567.1.l.b 2
3.b odd 2 1 CM 567.1.l.b 2
7.b odd 2 1 CM 567.1.l.b 2
7.c even 3 1 3969.1.k.b 2
7.c even 3 1 3969.1.t.c 2
7.d odd 6 1 3969.1.k.b 2
7.d odd 6 1 3969.1.t.c 2
9.c even 3 1 63.1.d.a 1
9.c even 3 1 inner 567.1.l.b 2
9.d odd 6 1 63.1.d.a 1
9.d odd 6 1 inner 567.1.l.b 2
21.c even 2 1 RM 567.1.l.b 2
21.g even 6 1 3969.1.k.b 2
21.g even 6 1 3969.1.t.c 2
21.h odd 6 1 3969.1.k.b 2
21.h odd 6 1 3969.1.t.c 2
36.f odd 6 1 1008.1.f.a 1
36.h even 6 1 1008.1.f.a 1
45.h odd 6 1 1575.1.h.b 1
45.j even 6 1 1575.1.h.b 1
45.k odd 12 2 1575.1.e.b 2
45.l even 12 2 1575.1.e.b 2
63.g even 3 1 441.1.m.a 2
63.g even 3 1 3969.1.t.c 2
63.h even 3 1 441.1.m.a 2
63.h even 3 1 3969.1.k.b 2
63.i even 6 1 441.1.m.a 2
63.i even 6 1 3969.1.k.b 2
63.j odd 6 1 441.1.m.a 2
63.j odd 6 1 3969.1.k.b 2
63.k odd 6 1 441.1.m.a 2
63.k odd 6 1 3969.1.t.c 2
63.l odd 6 1 63.1.d.a 1
63.l odd 6 1 inner 567.1.l.b 2
63.n odd 6 1 441.1.m.a 2
63.n odd 6 1 3969.1.t.c 2
63.o even 6 1 63.1.d.a 1
63.o even 6 1 inner 567.1.l.b 2
63.s even 6 1 441.1.m.a 2
63.s even 6 1 3969.1.t.c 2
63.t odd 6 1 441.1.m.a 2
63.t odd 6 1 3969.1.k.b 2
252.s odd 6 1 1008.1.f.a 1
252.bi even 6 1 1008.1.f.a 1
315.z even 6 1 1575.1.h.b 1
315.bg odd 6 1 1575.1.h.b 1
315.cb even 12 2 1575.1.e.b 2
315.cf odd 12 2 1575.1.e.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
63.1.d.a 1 9.c even 3 1
63.1.d.a 1 9.d odd 6 1
63.1.d.a 1 63.l odd 6 1
63.1.d.a 1 63.o even 6 1
441.1.m.a 2 63.g even 3 1
441.1.m.a 2 63.h even 3 1
441.1.m.a 2 63.i even 6 1
441.1.m.a 2 63.j odd 6 1
441.1.m.a 2 63.k odd 6 1
441.1.m.a 2 63.n odd 6 1
441.1.m.a 2 63.s even 6 1
441.1.m.a 2 63.t odd 6 1
567.1.l.b 2 1.a even 1 1 trivial
567.1.l.b 2 3.b odd 2 1 CM
567.1.l.b 2 7.b odd 2 1 CM
567.1.l.b 2 9.c even 3 1 inner
567.1.l.b 2 9.d odd 6 1 inner
567.1.l.b 2 21.c even 2 1 RM
567.1.l.b 2 63.l odd 6 1 inner
567.1.l.b 2 63.o even 6 1 inner
1008.1.f.a 1 36.f odd 6 1
1008.1.f.a 1 36.h even 6 1
1008.1.f.a 1 252.s odd 6 1
1008.1.f.a 1 252.bi even 6 1
1575.1.e.b 2 45.k odd 12 2
1575.1.e.b 2 45.l even 12 2
1575.1.e.b 2 315.cb even 12 2
1575.1.e.b 2 315.cf odd 12 2
1575.1.h.b 1 45.h odd 6 1
1575.1.h.b 1 45.j even 6 1
1575.1.h.b 1 315.z even 6 1
1575.1.h.b 1 315.bg odd 6 1
3969.1.k.b 2 7.c even 3 1
3969.1.k.b 2 7.d odd 6 1
3969.1.k.b 2 21.g even 6 1
3969.1.k.b 2 21.h odd 6 1
3969.1.k.b 2 63.h even 3 1
3969.1.k.b 2 63.i even 6 1
3969.1.k.b 2 63.j odd 6 1
3969.1.k.b 2 63.t odd 6 1
3969.1.t.c 2 7.c even 3 1
3969.1.t.c 2 7.d odd 6 1
3969.1.t.c 2 21.g even 6 1
3969.1.t.c 2 21.h odd 6 1
3969.1.t.c 2 63.g even 3 1
3969.1.t.c 2 63.k odd 6 1
3969.1.t.c 2 63.n odd 6 1
3969.1.t.c 2 63.s even 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{1}^{\mathrm{new}}(567, [\chi])\).