Newform orbit 95.3.h.a

• Label: 95.3.h.a
• Level: $95$
• Weight: $3$
• Character orbit: 95.h
• Analytic conductor: $2.589$
• Analytic rank: $0$
• Dimension: $36$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	95.h (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.58856251142\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Relative dimension:	\(18\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 32 q^{4} - 2 q^{5} + 20 q^{6} - 44 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
69.1	−1.75802	−	3.04498i	1.12259	+	1.94438i	−4.18128	+	7.24219i	4.99876	−	0.111455i	3.94707	−	6.83653i		−	7.10625i	15.3389			1.97959	−	3.42875i	−9.12730	−	15.0252i
69.2	−1.71056	−	2.96278i	−0.826102	−	1.43085i	−3.85204	+	6.67193i	−0.955782	+	4.90780i	−2.82620	+	4.89512i			10.6356i	12.6721			3.13511	−	5.43017i	16.1756	−	5.56332i
69.3	−1.56182	−	2.70515i	−1.79906	−	3.11607i	−2.87858	+	4.98584i	−1.62717	−	4.72783i	−5.61963	+	9.73349i			0.492630i	5.48871			−1.97326	+	3.41779i	−10.2482	+	11.7858i
69.4	−1.53172	−	2.65301i	2.91330	+	5.04598i	−2.69232	+	4.66323i	−4.89099	−	1.03838i	8.92470	−	15.4580i			8.30369i	4.24174			−12.4746	+	21.6067i	4.73678	+	14.5664i
69.5	−1.02897	−	1.78222i	0.527811	+	0.914195i	−0.117545	+	0.203595i	−4.49243	+	2.19501i	1.08620	−	1.88135i		−	12.4496i	−7.74793			3.94283	−	6.82918i	8.53455	+	5.74793i
69.6	−0.657945	−	1.13959i	−1.77141	−	3.06817i	1.13422	−	1.96452i	4.99378	−	0.249321i	−2.33098	+	4.03737i		−	1.38287i	−8.24857			−1.77578	+	3.07574i	−3.56976	−	5.52684i
69.7	−0.627935	−	1.08762i	1.22839	+	2.12764i	1.21139	−	2.09820i	3.11888	+	3.90802i	1.54270	−	2.67204i			6.64549i	−8.06619			1.48210	−	2.56708i	2.29197	−	5.84612i
69.8	−0.551994	−	0.956082i	0.649860	+	1.12559i	1.39060	−	2.40860i	−1.14750	−	4.86654i	0.717438	−	1.24264i			3.62786i	−7.48638			3.65536	−	6.33128i	−4.01940	+	3.78341i
69.9	−0.0850185	−	0.147256i	−2.59532	−	4.49522i	1.98554	−	3.43906i	−4.74707	+	1.57014i	−0.441300	+	0.764354i			5.65360i	−1.35538			−8.97135	+	15.5388i	0.634802	+	0.565545i
69.10	0.0850185	+	0.147256i	2.59532	+	4.49522i	1.98554	−	3.43906i	3.73331	−	3.32601i	−0.441300	+	0.764354i		−	5.65360i	1.35538			−8.97135	+	15.5388i	0.807177	+	0.266982i
69.11	0.551994	+	0.956082i	−0.649860	−	1.12559i	1.39060	−	2.40860i	−3.64080	−	3.42703i	0.717438	−	1.24264i		−	3.62786i	7.48638			3.65536	−	6.33128i	1.26683	−	5.37261i
69.12	0.627935	+	1.08762i	−1.22839	−	2.12764i	1.21139	−	2.09820i	1.82500	+	4.65504i	1.54270	−	2.67204i		−	6.64549i	8.06619			1.48210	−	2.56708i	−3.91691	+	4.90796i
69.13	0.657945	+	1.13959i	1.77141	+	3.06817i	1.13422	−	1.96452i	−2.71281	+	4.20008i	−2.33098	+	4.03737i			1.38287i	8.24857			−1.77578	+	3.07574i	−6.57126	−	0.328079i
69.14	1.02897	+	1.78222i	−0.527811	−	0.914195i	−0.117545	+	0.203595i	4.14715	−	2.79306i	1.08620	−	1.88135i			12.4496i	7.74793			3.94283	−	6.82918i	9.24513	+	4.51718i
69.15	1.53172	+	2.65301i	−2.91330	−	5.04598i	−2.69232	+	4.66323i	1.54623	−	4.75491i	8.92470	−	15.4580i		−	8.30369i	−4.24174			−12.4746	+	21.6067i	14.9832	−	3.18101i
69.16	1.56182	+	2.70515i	1.79906	+	3.11607i	−2.87858	+	4.98584i	−3.28083	−	3.77308i	−5.61963	+	9.73349i		−	0.492630i	−5.48871			−1.97326	+	3.41779i	5.08269	−	14.7680i
69.17	1.71056	+	2.96278i	0.826102	+	1.43085i	−3.85204	+	6.67193i	4.72817	+	1.62617i	−2.82620	+	4.89512i		−	10.6356i	−12.6721			3.13511	−	5.43017i	3.26985	+	16.7902i
69.18	1.75802	+	3.04498i	−1.12259	−	1.94438i	−4.18128	+	7.24219i	−2.59590	+	4.27332i	3.94707	−	6.83653i			7.10625i	−15.3389			1.97959	−	3.42875i	−17.5758	−	0.391880i
84.1	−1.75802	+	3.04498i	1.12259	−	1.94438i	−4.18128	−	7.24219i	4.99876	+	0.111455i	3.94707	+	6.83653i			7.10625i	15.3389			1.97959	+	3.42875i	−9.12730	+	15.0252i
84.2	−1.71056	+	2.96278i	−0.826102	+	1.43085i	−3.85204	−	6.67193i	−0.955782	−	4.90780i	−2.82620	−	4.89512i		−	10.6356i	12.6721			3.13511	+	5.43017i	16.1756	+	5.56332i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
19.d	odd	6	1	inner
95.h	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	95.3.h.a	✓	36
5.b	even	2	1	inner	95.3.h.a	✓	36
19.d	odd	6	1	inner	95.3.h.a	✓	36
95.h	odd	6	1	inner	95.3.h.a	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.3.h.a	✓	36	1.a	even	1	1	trivial
95.3.h.a	✓	36	5.b	even	2	1	inner
95.3.h.a	✓	36	19.d	odd	6	1	inner
95.3.h.a	✓	36	95.h	odd	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(95, [\chi])\).