Newform orbit 936.2.cl.a

• Label: 936.2.cl.a
• Level: $936$
• Weight: $2$
• Character orbit: 936.cl
• Analytic conductor: $7.474$
• Analytic rank: $0$
• Dimension: $24$
• CM discriminant: -104
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.cl (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.47399762919\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{4} - 48 q^{16} + 60 q^{25} + 12 q^{27} + 48 q^{30} + 48 q^{42} - 84 q^{49} - 60 q^{51} - 192 q^{64} - 168 q^{75} - 96 q^{90}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
155.1	−1.22474	−	0.707107i	−1.68278	+	0.410175i	1.00000	+	1.73205i	2.22783	−	1.28624i	2.35102	+	0.687548i	2.15165	−	3.72676i		−	2.82843i	2.66351	−	1.38047i	−3.63804
155.2	−1.22474	−	0.707107i	−1.02543	−	1.39588i	1.00000	+	1.73205i	3.74302	−	2.16104i	0.268853	+	2.43469i	−1.88985	+	3.27332i		−	2.82843i	−0.896983	+	2.86276i	−6.11233
155.3	−1.22474	−	0.707107i	−0.696155	+	1.58599i	1.00000	+	1.73205i	−2.73310	+	1.57795i	1.97408	−	1.45018i	2.54847	−	4.41407i		−	2.82843i	−2.03074	−	2.20819i	4.46313
155.4	−1.22474	−	0.707107i	0.486170	−	1.66242i	1.00000	+	1.73205i	−3.85756	+	2.22716i	−1.77094	+	1.69227i	0.257522	−	0.446041i		−	2.82843i	−2.52728	−	1.61644i	6.29937
155.5	−1.22474	−	0.707107i	1.19661	+	1.25225i	1.00000	+	1.73205i	1.62973	−	0.940923i	−0.580075	−	2.37981i	−2.40917	+	4.17280i		−	2.82843i	−0.136235	+	2.99691i	−2.66133
155.6	−1.22474	−	0.707107i	1.72159	−	0.190107i	1.00000	+	1.73205i	−1.00993	+	0.583083i	−2.24293	−	0.984512i	−0.658612	+	1.14075i		−	2.82843i	2.92772	−	0.654573i	1.64921
155.7	1.22474	+	0.707107i	−1.68278	+	0.410175i	1.00000	+	1.73205i	−2.22783	+	1.28624i	−2.35102	−	0.687548i	−2.15165	+	3.72676i			2.82843i	2.66351	−	1.38047i	−3.63804
155.8	1.22474	+	0.707107i	−1.02543	−	1.39588i	1.00000	+	1.73205i	−3.74302	+	2.16104i	−0.268853	−	2.43469i	1.88985	−	3.27332i			2.82843i	−0.896983	+	2.86276i	−6.11233
155.9	1.22474	+	0.707107i	−0.696155	+	1.58599i	1.00000	+	1.73205i	2.73310	−	1.57795i	−1.97408	+	1.45018i	−2.54847	+	4.41407i			2.82843i	−2.03074	−	2.20819i	4.46313
155.10	1.22474	+	0.707107i	0.486170	−	1.66242i	1.00000	+	1.73205i	3.85756	−	2.22716i	1.77094	−	1.69227i	−0.257522	+	0.446041i			2.82843i	−2.52728	−	1.61644i	6.29937
155.11	1.22474	+	0.707107i	1.19661	+	1.25225i	1.00000	+	1.73205i	−1.62973	+	0.940923i	0.580075	+	2.37981i	2.40917	−	4.17280i			2.82843i	−0.136235	+	2.99691i	−2.66133
155.12	1.22474	+	0.707107i	1.72159	−	0.190107i	1.00000	+	1.73205i	1.00993	−	0.583083i	2.24293	+	0.984512i	0.658612	−	1.14075i			2.82843i	2.92772	−	0.654573i	1.64921
779.1	−1.22474	+	0.707107i	−1.68278	−	0.410175i	1.00000	−	1.73205i	2.22783	+	1.28624i	2.35102	−	0.687548i	2.15165	+	3.72676i			2.82843i	2.66351	+	1.38047i	−3.63804
779.2	−1.22474	+	0.707107i	−1.02543	+	1.39588i	1.00000	−	1.73205i	3.74302	+	2.16104i	0.268853	−	2.43469i	−1.88985	−	3.27332i			2.82843i	−0.896983	−	2.86276i	−6.11233
779.3	−1.22474	+	0.707107i	−0.696155	−	1.58599i	1.00000	−	1.73205i	−2.73310	−	1.57795i	1.97408	+	1.45018i	2.54847	+	4.41407i			2.82843i	−2.03074	+	2.20819i	4.46313
779.4	−1.22474	+	0.707107i	0.486170	+	1.66242i	1.00000	−	1.73205i	−3.85756	−	2.22716i	−1.77094	−	1.69227i	0.257522	+	0.446041i			2.82843i	−2.52728	+	1.61644i	6.29937
779.5	−1.22474	+	0.707107i	1.19661	−	1.25225i	1.00000	−	1.73205i	1.62973	+	0.940923i	−0.580075	+	2.37981i	−2.40917	−	4.17280i			2.82843i	−0.136235	−	2.99691i	−2.66133
779.6	−1.22474	+	0.707107i	1.72159	+	0.190107i	1.00000	−	1.73205i	−1.00993	−	0.583083i	−2.24293	+	0.984512i	−0.658612	−	1.14075i			2.82843i	2.92772	+	0.654573i	1.64921
779.7	1.22474	−	0.707107i	−1.68278	−	0.410175i	1.00000	−	1.73205i	−2.22783	−	1.28624i	−2.35102	+	0.687548i	−2.15165	−	3.72676i		−	2.82843i	2.66351	+	1.38047i	−3.63804
779.8	1.22474	−	0.707107i	−1.02543	+	1.39588i	1.00000	−	1.73205i	−3.74302	−	2.16104i	−0.268853	+	2.43469i	1.88985	+	3.27332i		−	2.82843i	−0.896983	−	2.86276i	−6.11233

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
104.h	odd	2	1	CM by \(\Q(\sqrt{-26}) \)
8.d	odd	2	1	inner
9.d	odd	6	1	inner
13.b	even	2	1	inner
72.l	even	6	1	inner
117.n	odd	6	1	inner
936.cl	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	936.2.cl.a	✓	24
8.d	odd	2	1	inner	936.2.cl.a	✓	24
9.d	odd	6	1	inner	936.2.cl.a	✓	24
13.b	even	2	1	inner	936.2.cl.a	✓	24
72.l	even	6	1	inner	936.2.cl.a	✓	24
104.h	odd	2	1	CM	936.2.cl.a	✓	24
117.n	odd	6	1	inner	936.2.cl.a	✓	24
936.cl	even	6	1	inner	936.2.cl.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
936.2.cl.a	✓	24	1.a	even	1	1	trivial
936.2.cl.a	✓	24	8.d	odd	2	1	inner
936.2.cl.a	✓	24	9.d	odd	6	1	inner
936.2.cl.a	✓	24	13.b	even	2	1	inner
936.2.cl.a	✓	24	72.l	even	6	1	inner
936.2.cl.a	✓	24	104.h	odd	2	1	CM
936.2.cl.a	✓	24	117.n	odd	6	1	inner
936.2.cl.a	✓	24	936.cl	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 - 60*T5^22 + 2250*T5^20 - 52564*T5^18 + 897255*T5^16 - 10696050*T5^14 + 95271072*T5^12 - 596915910*T5^10 + 2752043175*T5^8 - 8312788786*T5^6 + 17608262415*T5^4 - 19006195950*T5^2 + 13841287201