Properties

 Label 572.2.p.a Level $572$ Weight $2$ Character orbit 572.p Analytic conductor $4.567$ Analytic rank $0$ Dimension $24$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$572 = 2^{2} \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 572.p (of order $$6$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$4.56744299562$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ over $$\Q(\zeta_{6})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$24q - 2q^{3} + 6q^{7} - 14q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q - 2q^{3} + 6q^{7} - 14q^{9} - 2q^{13} - 6q^{19} + 10q^{23} - 40q^{25} - 8q^{27} - 8q^{29} + 8q^{35} + 18q^{37} + 36q^{41} + 10q^{43} - 30q^{45} + 14q^{49} + 44q^{51} + 16q^{53} - 24q^{59} + 6q^{61} - 6q^{63} - 24q^{65} - 54q^{67} + 10q^{69} + 18q^{71} + 6q^{75} - 16q^{77} - 32q^{79} - 4q^{81} + 52q^{87} - 18q^{89} - 18q^{91} + 30q^{93} - 12q^{95} + 42q^{97} + O(q^{100})$$

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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
309.1 0 −1.63981 2.84024i 0 0.829371i 0 0.846479 + 0.488715i 0 −3.87798 + 6.71686i 0
309.2 0 −1.16394 2.01600i 0 3.47989i 0 −0.907365 0.523867i 0 −1.20951 + 2.09493i 0
309.3 0 −1.07694 1.86531i 0 3.60411i 0 −3.54414 2.04621i 0 −0.819590 + 1.41957i 0
309.4 0 −0.909010 1.57445i 0 1.10453i 0 0.391551 + 0.226062i 0 −0.152598 + 0.264307i 0
309.5 0 −0.780208 1.35136i 0 0.661534i 0 3.95034 + 2.28073i 0 0.282552 0.489394i 0
309.6 0 −0.308986 0.535180i 0 3.59217i 0 −1.27174 0.734239i 0 1.30905 2.26735i 0
309.7 0 0.0659947 + 0.114306i 0 0.505374i 0 −3.35869 1.93914i 0 1.49129 2.58299i 0
309.8 0 0.196667 + 0.340638i 0 4.15244i 0 2.01581 + 1.16383i 0 1.42264 2.46409i 0
309.9 0 0.716368 + 1.24079i 0 2.80197i 0 4.48758 + 2.59090i 0 0.473633 0.820357i 0
309.10 0 0.994483 + 1.72249i 0 2.64929i 0 −0.165013 0.0952705i 0 −0.477992 + 0.827907i 0
309.11 0 1.44478 + 2.50242i 0 0.307799i 0 −1.50558 0.869246i 0 −2.67475 + 4.63280i 0
309.12 0 1.46061 + 2.52985i 0 2.68122i 0 2.06077 + 1.18978i 0 −2.76675 + 4.79215i 0
485.1 0 −1.63981 + 2.84024i 0 0.829371i 0 0.846479 0.488715i 0 −3.87798 6.71686i 0
485.2 0 −1.16394 + 2.01600i 0 3.47989i 0 −0.907365 + 0.523867i 0 −1.20951 2.09493i 0
485.3 0 −1.07694 + 1.86531i 0 3.60411i 0 −3.54414 + 2.04621i 0 −0.819590 1.41957i 0
485.4 0 −0.909010 + 1.57445i 0 1.10453i 0 0.391551 0.226062i 0 −0.152598 0.264307i 0
485.5 0 −0.780208 + 1.35136i 0 0.661534i 0 3.95034 2.28073i 0 0.282552 + 0.489394i 0
485.6 0 −0.308986 + 0.535180i 0 3.59217i 0 −1.27174 + 0.734239i 0 1.30905 + 2.26735i 0
485.7 0 0.0659947 0.114306i 0 0.505374i 0 −3.35869 + 1.93914i 0 1.49129 + 2.58299i 0
485.8 0 0.196667 0.340638i 0 4.15244i 0 2.01581 1.16383i 0 1.42264 + 2.46409i 0
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 485.12 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
13.e even 6 1 inner

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 572.2.p.a 24
13.e even 6 1 inner 572.2.p.a 24
13.f odd 12 1 7436.2.a.u 12
13.f odd 12 1 7436.2.a.v 12

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
572.2.p.a 24 1.a even 1 1 trivial
572.2.p.a 24 13.e even 6 1 inner
7436.2.a.u 12 13.f odd 12 1
7436.2.a.v 12 13.f odd 12 1

Hecke kernels

This newform subspace is the entire newspace $$S_{2}^{\mathrm{new}}(572, [\chi])$$.