Properties

 Label 567.4.c.c Level $567$ Weight $4$ Character orbit 567.c Analytic conductor $33.454$ Analytic rank $0$ Dimension $44$ CM no Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 567.c (of order $$2$$, degree $$1$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$33.4540829733$$ Analytic rank: $$0$$ Dimension: $$44$$ Twist minimal: no (minimal twist has level 63) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $$q$$-expansion, but we have computed the trace expansion.

 $$\operatorname{Tr}(f)(q) =$$ $$44q - 156q^{4} - 10q^{7} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$44q - 156q^{4} - 10q^{7} + 484q^{16} + 68q^{22} + 704q^{25} + 300q^{28} + 328q^{37} + 340q^{43} + 968q^{46} + 158q^{49} + 1076q^{58} - 808q^{64} + 1180q^{67} - 768q^{70} + 604q^{79} + 1224q^{85} - 2588q^{88} + 210q^{91} + O(q^{100})$$

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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
566.1 3.79291i 0 −6.38613 −19.9518 0 17.7014 5.44617i 6.12125i 0 75.6753i
566.2 3.79291i 0 −6.38613 −19.9518 0 17.7014 + 5.44617i 6.12125i 0 75.6753i
566.3 0.0979055i 0 7.99041 −18.1269 0 5.25594 + 17.7588i 1.56555i 0 1.77473i
566.4 0.0979055i 0 7.99041 −18.1269 0 5.25594 17.7588i 1.56555i 0 1.77473i
566.5 4.93216i 0 −16.3262 15.3130 0 −18.2376 + 3.22314i 41.0664i 0 75.5262i
566.6 4.93216i 0 −16.3262 15.3130 0 −18.2376 3.22314i 41.0664i 0 75.5262i
566.7 2.99283i 0 −0.957005 −15.6029 0 −4.16816 + 18.0451i 21.0785i 0 46.6969i
566.8 2.99283i 0 −0.957005 −15.6029 0 −4.16816 18.0451i 21.0785i 0 46.6969i
566.9 3.90742i 0 −7.26794 11.6534 0 −14.6430 + 11.3394i 2.86048i 0 45.5347i
566.10 3.90742i 0 −7.26794 11.6534 0 −14.6430 11.3394i 2.86048i 0 45.5347i
566.11 0.725795i 0 7.47322 11.0664 0 −17.8071 5.08977i 11.2304i 0 8.03191i
566.12 0.725795i 0 7.47322 11.0664 0 −17.8071 + 5.08977i 11.2304i 0 8.03191i
566.13 5.40164i 0 −21.1777 6.87906 0 3.04840 18.2677i 71.1815i 0 37.1582i
566.14 5.40164i 0 −21.1777 6.87906 0 3.04840 + 18.2677i 71.1815i 0 37.1582i
566.15 2.23715i 0 2.99518 5.51516 0 4.78094 + 17.8925i 24.5978i 0 12.3382i
566.16 2.23715i 0 2.99518 5.51516 0 4.78094 17.8925i 24.5978i 0 12.3382i
566.17 4.53315i 0 −12.5495 0.137506 0 14.6188 + 11.3707i 20.6235i 0 0.623335i
566.18 4.53315i 0 −12.5495 0.137506 0 14.6188 11.3707i 20.6235i 0 0.623335i
566.19 1.27659i 0 6.37032 3.19020 0 17.8588 + 4.90527i 18.3450i 0 4.07258i
566.20 1.27659i 0 6.37032 3.19020 0 17.8588 4.90527i 18.3450i 0 4.07258i
See all 44 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 566.44 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
7.b odd 2 1 inner
21.c even 2 1 inner

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 567.4.c.c 44
3.b odd 2 1 inner 567.4.c.c 44
7.b odd 2 1 inner 567.4.c.c 44
9.c even 3 1 63.4.o.a 44
9.c even 3 1 189.4.o.a 44
9.d odd 6 1 63.4.o.a 44
9.d odd 6 1 189.4.o.a 44
21.c even 2 1 inner 567.4.c.c 44
63.l odd 6 1 63.4.o.a 44
63.l odd 6 1 189.4.o.a 44
63.o even 6 1 63.4.o.a 44
63.o even 6 1 189.4.o.a 44

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
63.4.o.a 44 9.c even 3 1
63.4.o.a 44 9.d odd 6 1
63.4.o.a 44 63.l odd 6 1
63.4.o.a 44 63.o even 6 1
189.4.o.a 44 9.c even 3 1
189.4.o.a 44 9.d odd 6 1
189.4.o.a 44 63.l odd 6 1
189.4.o.a 44 63.o even 6 1
567.4.c.c 44 1.a even 1 1 trivial
567.4.c.c 44 3.b odd 2 1 inner
567.4.c.c 44 7.b odd 2 1 inner
567.4.c.c 44 21.c even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{2}^{22} + \cdots$$ acting on $$S_{4}^{\mathrm{new}}(567, [\chi])$$.