Newform orbit 67.2.g.a

• Label: 67.2.g.a
• Level: $67$
• Weight: $2$
• Character orbit: 67.g
• Analytic conductor: $0.535$
• Analytic rank: $0$
• Dimension: $100$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	67.g (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.534997693543\)
Analytic rank:	\(0\)
Dimension:	\(100\)
Relative dimension:	\(5\) over \(\Q(\zeta_{33})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 100 q - 24 q^{2} - 14 q^{3} - 18 q^{4} - 16 q^{5} - 16 q^{6} - 24 q^{7} + 23 q^{8} - 32 q^{9}+O(q^{10}) \)

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	−2.35399	−	0.224779i	−2.34599	−	1.50767i	3.52690	+	0.679755i	0.527155	+	3.66644i	5.18354	+	4.07638i	−0.158469	+	0.222538i	−3.61169	−	1.06049i	1.98432	+	4.34506i	−0.416779	−	8.74927i
4.2	−1.37012	−	0.130831i	1.93217	+	1.24173i	−0.103746	−	0.0199954i	0.237517	+	1.65197i	−2.48485	−	1.95411i	0.302319	−	0.424548i	2.78073	+	0.816496i	0.945143	+	2.06957i	−0.109299	−	2.29447i
4.3	−0.966721	−	0.0923106i	−1.06638	−	0.685322i	−1.03783	−	0.200025i	−0.504825	−	3.51114i	0.967631	+	0.760953i	−0.420321	+	0.590258i	2.84839	+	0.836362i	−0.578741	−	1.26727i	0.163910	+	3.44089i
4.4	1.15591	+	0.110376i	0.248251	+	0.159542i	−0.639923	−	0.123335i	0.193683	+	1.34710i	0.269346	+	0.211816i	1.04578	−	1.46859i	−2.95433	−	0.867470i	−1.21007	−	2.64968i	0.0751929	+	1.57849i
4.5	2.26513	+	0.216294i	−2.12033	−	1.36265i	3.12018	+	0.601365i	−0.00341068	−	0.0237218i	−4.50809	−	3.54520i	−2.98179	+	4.18734i	2.57101	+	0.754918i	1.39272	+	3.04964i	−0.00259476	−	0.0544707i
6.1	−0.781425	+	2.25778i	−0.665809	+	1.45792i	−2.91483	−	2.29225i	−0.581051	−	0.170612i	−2.77138	−	2.64250i	2.97894	−	0.574144i	3.43329	−	2.20644i	0.282357	+	0.325857i	0.839252	−	1.17856i
6.2	−0.679423	+	1.96306i	1.24231	−	2.72029i	−1.81990	−	1.43118i	2.54249	+	0.746543i	4.49604	+	4.28696i	−3.22458	+	0.621487i	0.550889	−	0.354035i	−3.89203	−	4.49164i	−3.19294	+	4.48386i
6.3	0.0129395	−	0.0373862i	0.683139	−	1.49586i	1.57088	+	1.23535i	−2.74654	−	0.806457i	−0.0470852	−	0.0448957i	0.431636	−	0.0831910i	0.133075	−	0.0855220i	0.193649	+	0.223483i	−0.0656892	+	0.0922475i
6.4	0.260812	−	0.753567i	−1.39815	+	3.06152i	1.07227	+	0.843239i	−1.62666	−	0.477630i	1.94241	+	1.85208i	1.76797	−	0.340749i	2.25677	−	1.45034i	−5.45350	−	6.29368i	−0.784178	+	1.10122i
6.5	0.672578	−	1.94329i	−0.117502	+	0.257292i	−1.75190	−	1.37771i	0.783826	+	0.230152i	0.420964	+	0.401388i	−4.02301	+	0.775373i	−0.395684	+	0.254291i	1.91219	+	2.20678i	0.974436	−	1.36840i
10.1	−1.86173	−	1.77515i	−0.395503	−	2.75079i	0.219695	+	4.61197i	0.754900	−	1.65300i	−4.14675	+	5.82329i	−0.561736	+	2.31551i	4.40882	−	5.08805i	−4.53192	+	1.33069i	−4.33974	+	1.73737i
10.2	−1.70724	−	1.62785i	0.328848	+	2.28719i	0.169609	+	3.56053i	−1.68411	+	3.68769i	3.16178	−	4.44010i	0.549774	−	2.26620i	2.41691	−	2.78926i	−2.24462	+	0.659079i	8.87819	−	3.55429i
10.3	−0.397903	−	0.379400i	−0.140449	−	0.976841i	−0.0807812	−	1.69581i	−0.210771	+	0.461524i	−0.314728	+	0.441974i	0.229068	−	0.944230i	−1.33132	+	1.53642i	1.94399	−	0.570806i	0.258968	−	0.103675i
10.4	0.212667	+	0.202777i	0.345421	+	2.40246i	−0.0910553	−	1.91149i	0.243782	−	0.533809i	−0.413704	+	0.580967i	−0.729591	+	3.00742i	0.753099	−	0.869123i	−2.77401	+	0.814522i	0.160089	−	0.0640899i
10.5	1.38159	+	1.31734i	−0.402703	−	2.80086i	0.0782330	+	1.64231i	−1.09559	+	2.39900i	3.13332	−	4.40014i	−0.489299	+	2.01692i	0.444821	−	0.513350i	−4.80419	+	1.41064i	−4.67395	+	1.87117i
16.1	−2.05026	−	0.395155i	0.685119	+	1.50020i	2.19068	+	0.877018i	−2.80825	+	0.824577i	−0.811860	−	3.34653i	1.51400	+	4.37441i	−0.631852	−	0.406067i	0.183365	−	0.211615i	6.08348	−	0.580902i
16.2	−1.73997	−	0.335352i	−0.0213748	−	0.0468043i	1.05830	+	0.423679i	2.73293	−	0.802460i	0.0214956	+	0.0886061i	−1.49092	−	4.30774i	1.28206	+	0.823932i	1.96285	−	2.26525i	−5.02432	+	0.479764i
16.3	0.337638	+	0.0650744i	1.00488	+	2.20037i	−1.74697	−	0.699382i	0.701509	−	0.205982i	0.196096	+	0.808321i	−0.183820	−	0.531114i	−1.12286	−	0.721621i	−1.86728	+	2.15495i	0.250260	−	0.0238969i
16.4	0.596449	+	0.114956i	−0.971298	−	2.12685i	−1.51420	−	0.606194i	2.65848	−	0.780602i	−0.334836	−	1.38021i	1.26311	+	3.64950i	−1.85546	−	1.19243i	−1.61547	+	1.86435i	1.67539	−	0.159980i
16.5	1.83015	+	0.352733i	−0.175328	−	0.383915i	1.36831	+	0.547788i	−3.11563	+	0.914831i	−0.185458	−	0.764467i	−0.147983	−	0.427569i	−0.824926	−	0.530148i	1.84793	−	2.13263i	−6.02477	+	0.575296i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
67.g	even	33	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	67.2.g.a	✓	100
3.b	odd	2	1		603.2.z.c		100
67.g	even	33	1	inner	67.2.g.a	✓	100
67.g	even	33	1		4489.2.a.p		50
67.h	odd	66	1		4489.2.a.q		50
201.o	odd	66	1		603.2.z.c		100

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
67.2.g.a	✓	100	1.a	even	1	1	trivial
67.2.g.a	✓	100	67.g	even	33	1	inner
603.2.z.c		100	3.b	odd	2	1
603.2.z.c		100	201.o	odd	66	1
4489.2.a.p		50	67.g	even	33	1
4489.2.a.q		50	67.h	odd	66	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(67, [\chi])\).