Newform orbit 935.2.m.a

• Label: 935.2.m.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.m
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $192$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(192\)
Relative dimension:	\(96\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 192 q + 4 q^{3}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
307.1	−1.98331	+	1.98331i	1.35651	−	1.35651i		−	5.86706i	0.381691	+	2.20325i			5.38076i	0.370653	−	0.370653i	7.66958	+	7.66958i		−	0.680226i	−5.12675	−	3.61272i
307.2	−1.93357	+	1.93357i	−1.61794	+	1.61794i		−	5.47735i	1.44624	−	1.70540i		−	6.25677i	−2.31381	+	2.31381i	6.72369	+	6.72369i		−	2.23543i	0.501110	+	6.09390i
307.3	−1.91042	+	1.91042i	0.349720	−	0.349720i		−	5.29943i	1.53419	−	1.62673i			1.33623i	0.639654	−	0.639654i	6.30331	+	6.30331i			2.75539i	0.176786	+	6.03870i
307.4	−1.88915	+	1.88915i	−2.37433	+	2.37433i		−	5.13775i	−2.20266	+	0.385059i		−	8.97090i	1.11237	−	1.11237i	5.92768	+	5.92768i		−	8.27485i	3.43372	−	4.88859i
307.5	−1.82164	+	1.82164i	0.371491	−	0.371491i		−	4.63674i	−2.05786	−	0.874774i			1.35344i	−3.21996	+	3.21996i	4.80318	+	4.80318i			2.72399i	5.34219	−	2.15515i
307.6	−1.80064	+	1.80064i	−1.60846	+	1.60846i		−	4.48457i	0.788805	+	2.09232i		−	5.79251i	1.78653	−	1.78653i	4.47381	+	4.47381i		−	2.17431i	−5.18785	−	2.34715i
307.7	−1.77503	+	1.77503i	−0.659367	+	0.659367i		−	4.30145i	−1.36631	−	1.77008i		−	2.34079i	3.04398	−	3.04398i	4.08513	+	4.08513i			2.13047i	5.56719	+	0.716697i
307.8	−1.75460	+	1.75460i	1.55283	−	1.55283i		−	4.15728i	−0.988863	−	2.00553i			5.44919i	−0.718353	+	0.718353i	3.78517	+	3.78517i		−	1.82253i	5.25398	+	1.78385i
307.9	−1.75382	+	1.75382i	−0.783648	+	0.783648i		−	4.15175i	1.76312	+	1.37528i		−	2.74875i	0.867717	−	0.867717i	3.77378	+	3.77378i			1.77179i	−5.50419	+	0.680205i
307.10	−1.70361	+	1.70361i	1.98463	−	1.98463i		−	3.80454i	2.22717	−	0.199281i			6.76204i	1.59539	−	1.59539i	3.07423	+	3.07423i		−	4.87749i	−3.45472	+	4.13372i
307.11	−1.69751	+	1.69751i	2.08427	−	2.08427i		−	3.76306i	−2.14465	−	0.632816i			7.07614i	3.34903	−	3.34903i	2.99281	+	2.99281i		−	5.68839i	4.71478	−	2.56636i
307.12	−1.61263	+	1.61263i	−0.620260	+	0.620260i		−	3.20117i	−0.391114	+	2.20160i		−	2.00050i	−2.55626	+	2.55626i	1.93704	+	1.93704i			2.23055i	−2.91964	−	4.18109i
307.13	−1.56517	+	1.56517i	1.91197	−	1.91197i		−	2.89953i	−1.95362	+	1.08783i			5.98513i	−1.63806	+	1.63806i	1.40791	+	1.40791i		−	4.31127i	1.35511	−	4.76039i
307.14	−1.55208	+	1.55208i	−1.63195	+	1.63195i		−	2.81791i	−0.990694	−	2.00463i		−	5.06583i	−2.49843	+	2.49843i	1.26946	+	1.26946i		−	2.32651i	4.64898	+	1.57370i
307.15	−1.49293	+	1.49293i	1.62974	−	1.62974i		−	2.45768i	0.392900	+	2.20128i			4.86619i	−1.34626	+	1.34626i	0.683278	+	0.683278i		−	2.31213i	−3.87293	−	2.69978i
307.16	−1.48250	+	1.48250i	−0.0178685	+	0.0178685i		−	2.39559i	2.21254	+	0.323546i		−	0.0529799i	−1.35769	+	1.35769i	0.586463	+	0.586463i			2.99936i	−3.75973	+	2.80042i
307.17	−1.42075	+	1.42075i	−0.776839	+	0.776839i		−	2.03705i	1.02106	−	1.98933i		−	2.20738i	2.35583	−	2.35583i	0.0526320	+	0.0526320i			1.79304i	1.37568	+	4.27700i
307.18	−1.41335	+	1.41335i	0.838474	−	0.838474i		−	1.99510i	0.298779	−	2.21602i			2.37011i	−0.901140	+	0.901140i	−0.00693176	−	0.00693176i			1.59392i	2.70972	+	3.55428i
307.19	−1.32425	+	1.32425i	0.775578	−	0.775578i		−	1.50729i	−1.08397	+	1.95576i			2.05412i	2.19249	−	2.19249i	−0.652468	−	0.652468i			1.79696i	−1.15447	−	4.02538i
307.20	−1.24971	+	1.24971i	−2.35724	+	2.35724i		−	1.12353i	0.832768	+	2.07521i		−	5.89171i	−3.50331	+	3.50331i	−1.09533	−	1.09533i		−	8.11314i	−3.63412	−	1.55269i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
11.b	odd	2	1	inner
55.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.m.a	✓	192
5.c	odd	4	1	inner	935.2.m.a	✓	192
11.b	odd	2	1	inner	935.2.m.a	✓	192
55.e	even	4	1	inner	935.2.m.a	✓	192

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.m.a	✓	192	1.a	even	1	1	trivial
935.2.m.a	✓	192	5.c	odd	4	1	inner
935.2.m.a	✓	192	11.b	odd	2	1	inner
935.2.m.a	✓	192	55.e	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(935, [\chi])\).