Newform orbit 25.3.f.a

• Label: 25.3.f.a
• Level: $25$
• Weight: $3$
• Character orbit: 25.f
• Analytic conductor: $0.681$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.681200660901\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(4\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−3.57427	−	0.566108i	1.61679	+	3.17313i	8.65068	+	2.81078i	−0.872190	+	4.92334i	−3.98250	−	12.2569i	−0.574149	−	0.574149i	−16.4311	−	8.37205i	−2.16466	+	2.97940i	5.90458	−	17.1036i
2.2	−1.86717	−	0.295731i	−2.19472	−	4.30737i	−0.405347	−	0.131705i	4.99561	+	0.209511i	2.82409	+	8.69166i	−3.57009	−	3.57009i	7.45551	+	3.79877i	−8.44662	+	11.6258i	−9.26571	−	1.86855i
2.3	0.287585	+	0.0455490i	1.72787	+	3.39113i	−3.72360	−	1.20987i	2.36408	−	4.40581i	0.342446	+	1.05394i	−2.38950	−	2.38950i	−2.05348	−	1.04630i	−3.22416	+	4.43767i	0.880552	−	1.15936i
2.4	1.80600	+	0.286042i	−0.665351	−	1.30583i	−0.624420	−	0.202886i	−3.20727	+	3.83580i	−0.828102	−	2.54863i	3.62927	+	3.62927i	−7.58652	−	3.86553i	4.02758	−	5.54349i	−6.88953	+	6.01004i
3.1	−1.69523	−	3.32707i	−0.0858318	−	0.541921i	−5.84445	+	8.04419i	2.26962	−	4.45520i	−1.65750	+	1.20425i	1.68463	−	1.68463i	21.9189	+	3.47161i	8.27320	−	2.68812i	−18.6703	+	0.00137996i
3.2	−0.395527	−	0.776265i	−0.296456	−	1.87175i	1.90500	−	2.62200i	1.22928	+	4.84653i	−1.33572	+	0.970456i	−5.60844	+	5.60844i	−6.23083	−	0.986866i	5.14394	−	1.67137i	3.27598	−	2.87118i
3.3	−0.259330	−	0.508965i	0.838638	+	5.29495i	2.15935	−	2.97209i	−3.73307	−	3.32629i	2.47746	−	1.79998i	1.66138	−	1.66138i	−4.32944	−	0.685716i	−18.7737	+	6.09994i	−0.724866	+	2.76261i
3.4	1.29583	+	2.54321i	−0.363254	−	2.29349i	−2.43759	+	3.35505i	−4.45624	−	2.26758i	5.36211	−	3.89580i	−3.40272	+	3.40272i	−0.414625	−	0.0656701i	3.43135	−	1.11491i	−0.00760491	−	14.2715i
8.1	−2.38234	−	1.21387i	−3.57679	−	0.566508i	1.85096	+	2.54762i	−4.45026	−	2.27929i	7.83348	+	5.69136i	6.54971	−	6.54971i	0.355933	+	2.24727i	3.91299	+	1.27141i	7.83532	+	10.8321i
8.2	−1.61837	−	0.824603i	3.42034	+	0.541729i	−0.411975	−	0.567034i	4.00059	−	2.99921i	−5.08868	−	3.69715i	−8.06323	+	8.06323i	1.33571	+	8.43332i	2.84577	+	0.924645i	−8.94762	+	1.55494i
8.3	0.972743	+	0.495637i	0.872241	+	0.138149i	−1.65057	−	2.27181i	−2.66494	+	4.23062i	0.779995	+	0.566699i	1.62783	−	1.62783i	−1.16272	−	7.34115i	−7.81779	−	2.54015i	−4.68915	+	2.79446i
8.4	2.70026	+	1.37585i	−4.42692	−	0.701156i	3.04732	+	4.19427i	1.95091	−	4.60369i	−10.9892	−	7.98410i	−4.77540	+	4.77540i	0.561510	+	3.54523i	10.5465	+	3.42677i	11.6020	−	9.74701i
12.1	−0.513943	−	3.24491i	2.81033	+	1.43193i	−6.46108	+	2.09933i	−4.99960	−	0.0628765i	3.20215	−	9.85519i	7.51823	+	7.51823i	4.16668	+	8.17758i	0.557438	+	0.767248i	2.36548	+	16.2556i
12.2	−0.312579	−	1.97355i	−4.02069	−	2.04864i	0.00704800	−	0.00229003i	4.93389	+	0.810386i	−2.78631	+	8.57538i	3.91191	+	3.91191i	−3.63528	−	7.13464i	6.67894	+	9.19277i	0.0571038	−	9.99057i
12.3	0.0933465	+	0.589367i	0.210730	+	0.107372i	3.46559	−	1.12604i	−3.31432	+	3.74370i	−0.0436108	+	0.134220i	−7.64532	−	7.64532i	2.07076	+	4.06409i	−5.25719	−	7.23590i	−2.51579	−	1.60389i
12.4	0.463000	+	2.92327i	−0.866921	−	0.441718i	−4.52691	+	1.47088i	0.953911	−	4.90816i	0.889877	−	2.73876i	4.44588	+	4.44588i	−1.02103	−	2.00389i	−4.73363	−	6.51528i	14.7895	+	0.516059i
13.1	−3.57427	+	0.566108i	1.61679	−	3.17313i	8.65068	−	2.81078i	−0.872190	−	4.92334i	−3.98250	+	12.2569i	−0.574149	+	0.574149i	−16.4311	+	8.37205i	−2.16466	−	2.97940i	5.90458	+	17.1036i
13.2	−1.86717	+	0.295731i	−2.19472	+	4.30737i	−0.405347	+	0.131705i	4.99561	−	0.209511i	2.82409	−	8.69166i	−3.57009	+	3.57009i	7.45551	−	3.79877i	−8.44662	−	11.6258i	−9.26571	+	1.86855i
13.3	0.287585	−	0.0455490i	1.72787	−	3.39113i	−3.72360	+	1.20987i	2.36408	+	4.40581i	0.342446	−	1.05394i	−2.38950	+	2.38950i	−2.05348	+	1.04630i	−3.22416	−	4.43767i	0.880552	+	1.15936i
13.4	1.80600	−	0.286042i	−0.665351	+	1.30583i	−0.624420	+	0.202886i	−3.20727	−	3.83580i	−0.828102	+	2.54863i	3.62927	−	3.62927i	−7.58652	+	3.86553i	4.02758	+	5.54349i	−6.88953	−	6.01004i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
25.f	odd	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	25.3.f.a	✓	32
3.b	odd	2	1		225.3.r.a		32
4.b	odd	2	1		400.3.bg.c		32
5.b	even	2	1		125.3.f.c		32
5.c	odd	4	1		125.3.f.a		32
5.c	odd	4	1		125.3.f.b		32
25.d	even	5	1		125.3.f.a		32
25.e	even	10	1		125.3.f.b		32
25.f	odd	20	1	inner	25.3.f.a	✓	32
25.f	odd	20	1		125.3.f.c		32
75.l	even	20	1		225.3.r.a		32
100.l	even	20	1		400.3.bg.c		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
25.3.f.a	✓	32	1.a	even	1	1	trivial
25.3.f.a	✓	32	25.f	odd	20	1	inner
125.3.f.a		32	5.c	odd	4	1
125.3.f.a		32	25.d	even	5	1
125.3.f.b		32	5.c	odd	4	1
125.3.f.b		32	25.e	even	10	1
125.3.f.c		32	5.b	even	2	1
125.3.f.c		32	25.f	odd	20	1
225.3.r.a		32	3.b	odd	2	1
225.3.r.a		32	75.l	even	20	1
400.3.bg.c		32	4.b	odd	2	1
400.3.bg.c		32	100.l	even	20	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(25, [\chi])\).