# Properties

 Label 280.2.x.a Level $280$ Weight $2$ Character orbit 280.x Analytic conductor $2.236$ Analytic rank $0$ Dimension $24$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 280.x (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.23581125660$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$24q + 4q^{7} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q + 4q^{7} + 8q^{11} - 8q^{15} + 16q^{21} - 32q^{23} + 8q^{25} + 12q^{35} - 8q^{37} + 16q^{43} - 24q^{51} - 16q^{53} + 20q^{63} - 48q^{65} - 32q^{67} - 32q^{71} - 40q^{77} - 72q^{81} + 16q^{85} - 64q^{91} + 72q^{93} - 24q^{95} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
97.1 0 −2.16993 2.16993i 0 0.272751 + 2.21937i 0 −1.63589 + 2.07939i 0 6.41716i 0
97.2 0 −2.16341 2.16341i 0 1.91827 1.14901i 0 −0.409966 2.61380i 0 6.36066i 0
97.3 0 −1.41195 1.41195i 0 −1.94983 1.09461i 0 0.0496428 + 2.64529i 0 0.987218i 0
97.4 0 −1.03893 1.03893i 0 1.21973 1.87411i 0 2.11557 + 1.58883i 0 0.841261i 0
97.5 0 −0.730185 0.730185i 0 −1.51201 + 1.64737i 0 2.41329 1.08445i 0 1.93366i 0
97.6 0 −0.0703127 0.0703127i 0 −2.16104 0.574360i 0 −2.58523 0.562657i 0 2.99011i 0
97.7 0 0.0703127 + 0.0703127i 0 2.16104 + 0.574360i 0 −0.562657 2.58523i 0 2.99011i 0
97.8 0 0.730185 + 0.730185i 0 1.51201 1.64737i 0 −1.08445 + 2.41329i 0 1.93366i 0
97.9 0 1.03893 + 1.03893i 0 −1.21973 + 1.87411i 0 1.58883 + 2.11557i 0 0.841261i 0
97.10 0 1.41195 + 1.41195i 0 1.94983 + 1.09461i 0 2.64529 + 0.0496428i 0 0.987218i 0
97.11 0 2.16341 + 2.16341i 0 −1.91827 + 1.14901i 0 −2.61380 0.409966i 0 6.36066i 0
97.12 0 2.16993 + 2.16993i 0 −0.272751 2.21937i 0 2.07939 1.63589i 0 6.41716i 0
153.1 0 −2.16993 + 2.16993i 0 0.272751 2.21937i 0 −1.63589 2.07939i 0 6.41716i 0
153.2 0 −2.16341 + 2.16341i 0 1.91827 + 1.14901i 0 −0.409966 + 2.61380i 0 6.36066i 0
153.3 0 −1.41195 + 1.41195i 0 −1.94983 + 1.09461i 0 0.0496428 2.64529i 0 0.987218i 0
153.4 0 −1.03893 + 1.03893i 0 1.21973 + 1.87411i 0 2.11557 1.58883i 0 0.841261i 0
153.5 0 −0.730185 + 0.730185i 0 −1.51201 1.64737i 0 2.41329 + 1.08445i 0 1.93366i 0
153.6 0 −0.0703127 + 0.0703127i 0 −2.16104 + 0.574360i 0 −2.58523 + 0.562657i 0 2.99011i 0
153.7 0 0.0703127 0.0703127i 0 2.16104 0.574360i 0 −0.562657 + 2.58523i 0 2.99011i 0
153.8 0 0.730185 0.730185i 0 1.51201 + 1.64737i 0 −1.08445 2.41329i 0 1.93366i 0
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 153.12 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
7.b odd 2 1 inner
35.f even 4 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 280.2.x.a 24
4.b odd 2 1 560.2.bj.d 24
5.b even 2 1 1400.2.x.b 24
5.c odd 4 1 inner 280.2.x.a 24
5.c odd 4 1 1400.2.x.b 24
7.b odd 2 1 inner 280.2.x.a 24
20.e even 4 1 560.2.bj.d 24
28.d even 2 1 560.2.bj.d 24
35.c odd 2 1 1400.2.x.b 24
35.f even 4 1 inner 280.2.x.a 24
35.f even 4 1 1400.2.x.b 24
140.j odd 4 1 560.2.bj.d 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.2.x.a 24 1.a even 1 1 trivial
280.2.x.a 24 5.c odd 4 1 inner
280.2.x.a 24 7.b odd 2 1 inner
280.2.x.a 24 35.f even 4 1 inner
560.2.bj.d 24 4.b odd 2 1
560.2.bj.d 24 20.e even 4 1
560.2.bj.d 24 28.d even 2 1
560.2.bj.d 24 140.j odd 4 1
1400.2.x.b 24 5.b even 2 1
1400.2.x.b 24 5.c odd 4 1
1400.2.x.b 24 35.c odd 2 1
1400.2.x.b 24 35.f even 4 1

## Hecke kernels

This newform subspace is the entire newspace $$S_{2}^{\mathrm{new}}(280, [\chi])$$.