Newform orbit 25.4.e.a

• Label: 25.4.e.a
• Level: $25$
• Weight: $4$
• Character orbit: 25.e
• Analytic conductor: $1.475$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.47504775014\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−4.95462	−	1.60985i	−1.70326	+	2.34434i	15.4845	+	11.2501i	11.0057	−	1.96864i	12.2131	−	8.87330i			24.5811i	−34.1117	−	46.9507i	5.74864	+	17.6925i	−57.6981	−	7.96365i
4.2	−2.51328	−	0.816614i	1.75639	−	2.41747i	−0.822422	−	0.597525i	−5.31827	−	9.83443i	−6.38844	+	4.64147i		−	26.3705i	14.0054	+	19.2767i	5.58423	+	17.1865i	5.33537	+	29.0596i
4.3	−1.48841	−	0.483614i	−4.16357	+	5.73067i	−4.49065	−	3.26265i	−5.33345	+	9.82621i	8.96855	−	6.51603i			1.18261i	12.4652	+	17.1569i	−7.16175	−	22.0416i	12.6905	−	12.0461i
4.4	0.331937	+	0.107853i	3.76234	−	5.17842i	−6.37359	−	4.63068i	10.0178	+	4.96433i	1.80737	−	1.31313i			14.4107i	−3.25738	−	4.48340i	−4.31736	−	13.2875i	2.78985	+	2.72829i
4.5	3.33666	+	1.08415i	−3.80499	+	5.23712i	3.48577	+	2.53256i	10.7075	−	3.21691i	−18.3737	+	13.3493i		−	25.7483i	−7.61219	−	10.4773i	−4.60602	−	14.1759i	39.2150	+	0.874818i
4.6	3.47870	+	1.13030i	1.22604	−	1.68750i	4.35165	+	3.16166i	−11.1800	−	0.0808329i	6.17240	−	4.48451i			8.69522i	−5.63517	−	7.75614i	6.99898	+	21.5406i	−38.8007	−	12.9180i
9.1	−2.42187	+	3.33341i	−3.56321	+	1.15776i	−2.77407	−	8.53772i	−8.01402	−	7.79587i	4.77034	−	14.6816i			26.4674i	3.82887	+	1.24408i	−10.4874	+	7.61952i	45.3957	−	7.83348i
9.2	−2.23725	+	3.07931i	8.89950	−	2.89162i	−2.00472	−	6.16988i	−3.48187	+	10.6243i	−11.0062	+	33.8735i		−	4.54748i	−5.47554	−	1.77911i	48.9961	−	35.5978i	−24.9258	−	34.4910i
9.3	−0.442260	+	0.608718i	−6.75579	+	2.19509i	2.29719	+	7.07003i	1.00498	+	11.1351i	1.65162	−	5.08317i		−	18.3105i	−11.0443	−	3.58852i	18.9788	−	13.7889i	−7.22259	−	4.31284i
9.4	−0.217515	+	0.299383i	2.64413	−	0.859131i	2.42982	+	7.47821i	7.78705	−	8.02258i	−0.317928	+	0.978483i			0.707538i	−5.58294	−	1.81401i	−15.5901	+	11.3269i	0.708030	+	4.07634i
9.5	1.81265	−	2.49489i	3.16804	−	1.02936i	−0.466674	−	1.43628i	−10.8670	+	2.62823i	3.17440	−	9.76980i		−	5.10302i	19.0341	+	6.18456i	−12.8665	+	9.34809i	−13.1409	+	31.8762i
9.6	2.81526	−	3.87487i	−3.96562	+	1.28851i	−4.61680	−	14.2091i	11.1717	+	0.439337i	−6.17144	+	18.9937i			14.5499i	−31.6143	−	10.2721i	−7.77757	+	5.65074i	33.1536	−	42.0521i
14.1	−2.42187	−	3.33341i	−3.56321	−	1.15776i	−2.77407	+	8.53772i	−8.01402	+	7.79587i	4.77034	+	14.6816i		−	26.4674i	3.82887	−	1.24408i	−10.4874	−	7.61952i	45.3957	+	7.83348i
14.2	−2.23725	−	3.07931i	8.89950	+	2.89162i	−2.00472	+	6.16988i	−3.48187	−	10.6243i	−11.0062	−	33.8735i			4.54748i	−5.47554	+	1.77911i	48.9961	+	35.5978i	−24.9258	+	34.4910i
14.3	−0.442260	−	0.608718i	−6.75579	−	2.19509i	2.29719	−	7.07003i	1.00498	−	11.1351i	1.65162	+	5.08317i			18.3105i	−11.0443	+	3.58852i	18.9788	+	13.7889i	−7.22259	+	4.31284i
14.4	−0.217515	−	0.299383i	2.64413	+	0.859131i	2.42982	−	7.47821i	7.78705	+	8.02258i	−0.317928	−	0.978483i		−	0.707538i	−5.58294	+	1.81401i	−15.5901	−	11.3269i	0.708030	−	4.07634i
14.5	1.81265	+	2.49489i	3.16804	+	1.02936i	−0.466674	+	1.43628i	−10.8670	−	2.62823i	3.17440	+	9.76980i			5.10302i	19.0341	−	6.18456i	−12.8665	−	9.34809i	−13.1409	−	31.8762i
14.6	2.81526	+	3.87487i	−3.96562	−	1.28851i	−4.61680	+	14.2091i	11.1717	−	0.439337i	−6.17144	−	18.9937i		−	14.5499i	−31.6143	+	10.2721i	−7.77757	−	5.65074i	33.1536	+	42.0521i
19.1	−4.95462	+	1.60985i	−1.70326	−	2.34434i	15.4845	−	11.2501i	11.0057	+	1.96864i	12.2131	+	8.87330i		−	24.5811i	−34.1117	+	46.9507i	5.74864	−	17.6925i	−57.6981	+	7.96365i
19.2	−2.51328	+	0.816614i	1.75639	+	2.41747i	−0.822422	+	0.597525i	−5.31827	+	9.83443i	−6.38844	−	4.64147i			26.3705i	14.0054	−	19.2767i	5.58423	−	17.1865i	5.33537	−	29.0596i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
25.e	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	25.4.e.a	✓	24
3.b	odd	2	1		225.4.m.a		24
5.b	even	2	1		125.4.e.a		24
5.c	odd	4	2		125.4.d.b		48
25.d	even	5	1		125.4.e.a		24
25.e	even	10	1	inner	25.4.e.a	✓	24
25.f	odd	20	2		125.4.d.b		48
25.f	odd	20	2		625.4.a.g		24
75.h	odd	10	1		225.4.m.a		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
25.4.e.a	✓	24	1.a	even	1	1	trivial
25.4.e.a	✓	24	25.e	even	10	1	inner
125.4.d.b		48	5.c	odd	4	2
125.4.d.b		48	25.f	odd	20	2
125.4.e.a		24	5.b	even	2	1
125.4.e.a		24	25.d	even	5	1
225.4.m.a		24	3.b	odd	2	1
225.4.m.a		24	75.h	odd	10	1
625.4.a.g		24	25.f	odd	20	2

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(25, [\chi])\).