# Properties

 Label 280.2.bg.a Level $280$ Weight $2$ Character orbit 280.bg 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.bg (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.23581125660$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$24q + 14q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q + 14q^{9} - 2q^{11} + 12q^{15} - 10q^{19} - 10q^{21} - 2q^{25} + 12q^{29} + 4q^{31} - 28q^{35} + 20q^{39} + 24q^{41} - 8q^{45} - 30q^{49} - 12q^{55} - 48q^{59} - 18q^{61} - 26q^{65} - 60q^{69} + 16q^{71} - 14q^{75} - 44q^{79} + 12q^{81} - 44q^{85} + 30q^{89} + 44q^{91} - 26q^{95} - 44q^{99} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
9.1 0 −2.63533 + 1.52151i 0 −2.07968 + 0.821533i 0 0.629537 + 2.56976i 0 3.12998 5.42128i 0
9.2 0 −2.20343 + 1.27215i 0 −0.474541 2.18513i 0 2.64391 + 0.0988222i 0 1.73675 3.00813i 0
9.3 0 −1.82577 + 1.05411i 0 1.46656 1.68796i 0 −1.44930 2.21349i 0 0.722285 1.25103i 0
9.4 0 −1.76528 + 1.01918i 0 2.04540 + 0.903506i 0 −2.27974 + 1.34267i 0 0.577473 1.00021i 0
9.5 0 −0.650755 + 0.375714i 0 −0.702823 + 2.12274i 0 0.543003 2.58943i 0 −1.21768 + 2.10908i 0
9.6 0 −0.277116 + 0.159993i 0 −2.00685 0.986173i 0 −1.50695 2.17465i 0 −1.44880 + 2.50940i 0
9.7 0 0.277116 0.159993i 0 1.85748 + 1.24490i 0 1.50695 + 2.17465i 0 −1.44880 + 2.50940i 0
9.8 0 0.650755 0.375714i 0 −1.48694 + 1.67003i 0 −0.543003 + 2.58943i 0 −1.21768 + 2.10908i 0
9.9 0 1.76528 1.01918i 0 −1.80516 1.31962i 0 2.27974 1.34267i 0 0.577473 1.00021i 0
9.10 0 1.82577 1.05411i 0 0.728531 2.11406i 0 1.44930 + 2.21349i 0 0.722285 1.25103i 0
9.11 0 2.20343 1.27215i 0 2.12965 0.681602i 0 −2.64391 0.0988222i 0 1.73675 3.00813i 0
9.12 0 2.63533 1.52151i 0 0.328373 + 2.21183i 0 −0.629537 2.56976i 0 3.12998 5.42128i 0
249.1 0 −2.63533 1.52151i 0 −2.07968 0.821533i 0 0.629537 2.56976i 0 3.12998 + 5.42128i 0
249.2 0 −2.20343 1.27215i 0 −0.474541 + 2.18513i 0 2.64391 0.0988222i 0 1.73675 + 3.00813i 0
249.3 0 −1.82577 1.05411i 0 1.46656 + 1.68796i 0 −1.44930 + 2.21349i 0 0.722285 + 1.25103i 0
249.4 0 −1.76528 1.01918i 0 2.04540 0.903506i 0 −2.27974 1.34267i 0 0.577473 + 1.00021i 0
249.5 0 −0.650755 0.375714i 0 −0.702823 2.12274i 0 0.543003 + 2.58943i 0 −1.21768 2.10908i 0
249.6 0 −0.277116 0.159993i 0 −2.00685 + 0.986173i 0 −1.50695 + 2.17465i 0 −1.44880 2.50940i 0
249.7 0 0.277116 + 0.159993i 0 1.85748 1.24490i 0 1.50695 2.17465i 0 −1.44880 2.50940i 0
249.8 0 0.650755 + 0.375714i 0 −1.48694 1.67003i 0 −0.543003 2.58943i 0 −1.21768 2.10908i 0
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 249.12 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.b even 2 1 inner
7.c even 3 1 inner
35.j even 6 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 280.2.bg.a 24
4.b odd 2 1 560.2.bw.f 24
5.b even 2 1 inner 280.2.bg.a 24
5.c odd 4 1 1400.2.q.n 12
5.c odd 4 1 1400.2.q.o 12
7.c even 3 1 inner 280.2.bg.a 24
7.c even 3 1 1960.2.g.f 12
7.d odd 6 1 1960.2.g.e 12
20.d odd 2 1 560.2.bw.f 24
28.g odd 6 1 560.2.bw.f 24
35.i odd 6 1 1960.2.g.e 12
35.j even 6 1 inner 280.2.bg.a 24
35.j even 6 1 1960.2.g.f 12
35.k even 12 1 9800.2.a.cw 6
35.k even 12 1 9800.2.a.cy 6
35.l odd 12 1 1400.2.q.n 12
35.l odd 12 1 1400.2.q.o 12
35.l odd 12 1 9800.2.a.cv 6
35.l odd 12 1 9800.2.a.cx 6
140.p odd 6 1 560.2.bw.f 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.2.bg.a 24 1.a even 1 1 trivial
280.2.bg.a 24 5.b even 2 1 inner
280.2.bg.a 24 7.c even 3 1 inner
280.2.bg.a 24 35.j even 6 1 inner
560.2.bw.f 24 4.b odd 2 1
560.2.bw.f 24 20.d odd 2 1
560.2.bw.f 24 28.g odd 6 1
560.2.bw.f 24 140.p odd 6 1
1400.2.q.n 12 5.c odd 4 1
1400.2.q.n 12 35.l odd 12 1
1400.2.q.o 12 5.c odd 4 1
1400.2.q.o 12 35.l odd 12 1
1960.2.g.e 12 7.d odd 6 1
1960.2.g.e 12 35.i odd 6 1
1960.2.g.f 12 7.c even 3 1
1960.2.g.f 12 35.j even 6 1
9800.2.a.cv 6 35.l odd 12 1
9800.2.a.cw 6 35.k even 12 1
9800.2.a.cx 6 35.l odd 12 1
9800.2.a.cy 6 35.k even 12 1

## Hecke kernels

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