Newform orbit 280.3.bp.a

• Label: 280.3.bp.a
• Level: $280$
• Weight: $3$
• Character orbit: 280.bp
• Analytic conductor: $7.629$
• Analytic rank: $0$
• Dimension: $368$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	280.bp (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.62944740209\)
Analytic rank:	\(0\)
Dimension:	\(368\)
Relative dimension:	\(92\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 368 q - 2 q^{2} - 12 q^{3} + 4 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−1.99995	−	0.0141341i	0.644159	+	2.40403i	3.99960	+	0.0565350i	−3.72006	+	3.34083i	−1.25431	−	4.81705i	6.04778	−	3.52481i	−7.99820	−	0.169598i	2.42979	−	1.40284i	7.48715	−	6.62892i
3.2	−1.99844	−	0.0789782i	−1.34023	−	5.00179i	3.98752	+	0.315666i	3.39814	−	3.66778i	2.28333	+	10.1016i	−0.749547	+	6.95975i	−7.94390	−	0.945767i	−15.4275	+	8.90707i	−7.08066	+	7.06147i
3.3	−1.99553	+	0.133651i	−0.394822	−	1.47350i	3.96427	−	0.533410i	4.87784	+	1.09848i	0.984815	+	2.88764i	−4.43163	−	5.41855i	−7.83954	+	1.59427i	5.77892	−	3.33646i	−9.88069	−	1.54012i
3.4	−1.99254	−	0.172539i	0.0777985	+	0.290348i	3.94046	+	0.687583i	−3.45340	−	3.61581i	−0.104921	−	0.591954i	−6.96306	−	0.718194i	−7.73291	−	2.04992i	7.71598	−	4.45482i	6.25718	+	7.80050i
3.5	−1.98879	−	0.211493i	1.48069	+	5.52601i	3.91054	+	0.841231i	2.19690	+	4.49151i	−1.77606	−	11.3032i	−4.57928	−	5.29435i	−7.59932	−	2.50008i	−20.5502	+	11.8646i	−3.41924	−	9.39727i
3.6	−1.97443	−	0.318798i	−0.761913	−	2.84350i	3.79674	+	1.25889i	−1.30372	+	4.82704i	0.597841	+	5.85718i	−4.62448	+	5.25492i	−7.09505	−	3.69598i	0.289262	−	0.167005i	4.11295	−	9.11502i
3.7	−1.95969	+	0.399524i	0.807586	+	3.01395i	3.68076	−	1.56589i	4.99316	+	0.261357i	−2.78676	−	5.58376i	0.863102	+	6.94659i	−6.58753	+	4.53921i	−0.637478	+	0.368048i	−9.88947	+	1.48271i
3.8	−1.95789	+	0.408236i	0.567932	+	2.11955i	3.66669	−	1.59857i	0.103149	−	4.99894i	−1.97723	−	3.91800i	6.67098	−	2.12087i	−6.52639	+	4.62669i	3.62427	−	2.09248i	1.83879	+	9.82949i
3.9	−1.88816	+	0.659443i	−0.860768	−	3.21243i	3.13027	−	2.49026i	−4.98210	−	0.422729i	3.74368	+	5.49795i	5.32150	+	4.54771i	−4.26825	+	6.76624i	−1.78457	+	1.03032i	9.68575	−	2.48723i
3.10	−1.86930	−	0.711127i	−0.761913	−	2.84350i	2.98860	+	2.65863i	1.30372	−	4.82704i	−0.597841	+	5.85718i	4.62448	−	5.25492i	−3.69598	−	7.09505i	0.289262	−	0.167005i	−5.86969	+	8.09610i
3.11	−1.82809	−	0.811234i	1.48069	+	5.52601i	2.68380	+	2.96601i	−2.19690	−	4.49151i	1.77606	−	11.3032i	4.57928	+	5.29435i	−2.50008	−	7.59932i	−20.5502	+	11.8646i	0.372462	+	9.99306i
3.12	−1.82419	+	0.819965i	−1.26142	−	4.70768i	2.65532	−	2.99154i	−4.11946	−	2.83373i	6.16120	+	7.55337i	−3.81527	−	5.86888i	−2.39083	+	7.63439i	−12.7768	+	7.37671i	9.83823	+	1.79144i
3.13	−1.81186	−	0.846849i	0.0777985	+	0.290348i	2.56569	+	3.06875i	3.45340	+	3.61581i	0.104921	−	0.591954i	6.96306	+	0.718194i	−2.04992	−	7.73291i	7.71598	−	4.45482i	−3.19504	−	9.47585i
3.14	−1.79230	+	0.887499i	−0.106711	−	0.398249i	2.42469	−	3.18133i	−2.22933	+	4.47550i	0.544703	+	0.619077i	−0.940345	−	6.93655i	−1.52235	+	7.85382i	7.64701	−	4.41501i	0.0236378	−	9.99997i
3.15	−1.77019	−	0.930823i	−1.34023	−	5.00179i	2.26714	+	3.29546i	−3.39814	+	3.66778i	−2.28333	+	10.1016i	0.749547	−	6.95975i	−0.945767	−	7.94390i	−15.4275	+	8.90707i	9.42941	−	3.32960i
3.16	−1.73907	−	0.987735i	0.644159	+	2.40403i	2.04876	+	3.43549i	3.72006	−	3.34083i	1.25431	−	4.81705i	−6.04778	+	3.52481i	−0.169598	−	7.99820i	2.42979	−	1.40284i	−9.76932	+	2.13553i
3.17	−1.73734	+	0.990778i	1.07078	+	3.99619i	2.03672	−	3.44264i	−4.99983	+	0.0417196i	−5.81964	−	5.88185i	−5.67109	+	4.10350i	−0.127590	+	7.99898i	−7.02873	+	4.05804i	8.64508	−	5.02620i
3.18	−1.66135	−	1.11351i	−0.394822	−	1.47350i	1.52019	+	3.69987i	−4.87784	−	1.09848i	−0.984815	+	2.88764i	4.43163	+	5.41855i	1.59427	−	7.83954i	5.77892	−	3.33646i	6.88065	+	7.25649i
3.19	−1.64918	+	1.13146i	−0.180085	−	0.672088i	1.43961	−	3.73196i	1.46030	+	4.78200i	1.05743	+	0.904638i	0.296125	+	6.99373i	1.84836	+	7.78354i	7.37496	−	4.25793i	−7.81892	−	6.23413i
3.20	−1.62709	+	1.16301i	1.11324	+	4.15466i	1.29484	−	3.78463i	2.04089	−	4.56451i	−6.64322	−	5.46530i	−2.76079	−	6.43257i	2.29472	+	7.66383i	−8.22765	+	4.75023i	1.98784	+	9.80043i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.d	odd	6	1	inner
8.d	odd	2	1	inner
35.k	even	12	1	inner
40.k	even	4	1	inner
56.m	even	6	1	inner
280.bp	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	280.3.bp.a	✓	368
5.c	odd	4	1	inner	280.3.bp.a	✓	368
7.d	odd	6	1	inner	280.3.bp.a	✓	368
8.d	odd	2	1	inner	280.3.bp.a	✓	368
35.k	even	12	1	inner	280.3.bp.a	✓	368
40.k	even	4	1	inner	280.3.bp.a	✓	368
56.m	even	6	1	inner	280.3.bp.a	✓	368
280.bp	odd	12	1	inner	280.3.bp.a	✓	368

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
280.3.bp.a	✓	368	1.a	even	1	1	trivial
280.3.bp.a	✓	368	5.c	odd	4	1	inner
280.3.bp.a	✓	368	7.d	odd	6	1	inner
280.3.bp.a	✓	368	8.d	odd	2	1	inner
280.3.bp.a	✓	368	35.k	even	12	1	inner
280.3.bp.a	✓	368	40.k	even	4	1	inner
280.3.bp.a	✓	368	56.m	even	6	1	inner
280.3.bp.a	✓	368	280.bp	odd	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(280, [\chi])\).