Newform orbit 504.2.cq.a

• Label: 504.2.cq.a
• Level: $504$
• Weight: $2$
• Character orbit: 504.cq
• Analytic conductor: $4.024$
• Analytic rank: $0$
• Dimension: $184$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cq (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.02446026187\)
Analytic rank:	\(0\)
Dimension:	\(184\)
Relative dimension:	\(92\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 184 q - 2 q^{2} - 2 q^{4} - 2 q^{6} - 2 q^{7} - 8 q^{8} - 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
277.1	−1.41195	−	0.0799747i	1.37829	+	1.04896i	1.98721	+	0.225841i	3.10331	+	1.79170i	−1.86219	−	1.59130i	−1.70224	−	2.02544i	−2.78778	−	0.477802i	0.799378	+	2.89154i	−4.23843	−	2.77797i
277.2	−1.41195	+	0.0799747i	−1.37829	−	1.04896i	1.98721	−	0.225841i	−3.10331	−	1.79170i	2.02997	+	1.37085i	−1.70224	−	2.02544i	−2.78778	+	0.477802i	0.799378	+	2.89154i	4.52501	+	2.28160i
277.3	−1.40384	−	0.171013i	−1.37821	+	1.04907i	1.94151	+	0.480149i	0.213745	+	0.123406i	2.11418	−	1.23703i	−2.18219	+	1.49601i	−2.64345	−	1.00607i	0.798909	−	2.89167i	−0.278959	−	0.209795i
277.4	−1.40384	+	0.171013i	1.37821	−	1.04907i	1.94151	−	0.480149i	−0.213745	−	0.123406i	−1.75537	+	1.70841i	−2.18219	+	1.49601i	−2.64345	+	1.00607i	0.798909	−	2.89167i	0.321167	+	0.136688i
277.5	−1.38793	−	0.271374i	1.73202	+	0.00998187i	1.85271	+	0.753297i	−1.80782	−	1.04374i	−2.40122	−	0.483879i	2.62626	−	0.320557i	−2.36702	−	1.54830i	2.99980	+	0.0345777i	2.22588	+	1.93924i
277.6	−1.38793	+	0.271374i	−1.73202	−	0.00998187i	1.85271	−	0.753297i	1.80782	+	1.04374i	2.40664	−	0.456171i	2.62626	−	0.320557i	−2.36702	+	1.54830i	2.99980	+	0.0345777i	−2.79237	−	0.958051i
277.7	−1.38729	−	0.274643i	−0.170331	−	1.72366i	1.84914	+	0.762020i	−2.08943	−	1.20633i	−0.237093	+	2.43799i	0.664788	+	2.56087i	−2.35601	−	1.56500i	−2.94197	+	0.587183i	2.56733	+	2.24738i
277.8	−1.38729	+	0.274643i	0.170331	+	1.72366i	1.84914	−	0.762020i	2.08943	+	1.20633i	−0.709689	−	2.34443i	0.664788	+	2.56087i	−2.35601	+	1.56500i	−2.94197	+	0.587183i	−3.22995	−	1.09968i
277.9	−1.37280	−	0.339745i	−0.0247783	+	1.73187i	1.76915	+	0.932801i	−0.736012	−	0.424937i	0.622410	−	2.36909i	1.20653	−	2.35463i	−2.11177	−	1.88161i	−2.99877	−	0.0858258i	0.866026	+	0.833408i
277.10	−1.37280	+	0.339745i	0.0247783	−	1.73187i	1.76915	−	0.932801i	0.736012	+	0.424937i	0.554379	+	2.38593i	1.20653	−	2.35463i	−2.11177	+	1.88161i	−2.99877	−	0.0858258i	−1.15477	−	0.333296i
277.11	−1.28938	−	0.580936i	1.21975	−	1.22972i	1.32503	+	1.49810i	3.55178	+	2.05062i	−2.28712	+	0.876982i	2.40176	+	1.10974i	−0.838168	−	2.70138i	−0.0244139	−	2.99990i	−3.38833	−	4.70739i
277.12	−1.28938	+	0.580936i	−1.21975	+	1.22972i	1.32503	−	1.49810i	−3.55178	−	2.05062i	0.858341	−	2.29418i	2.40176	+	1.10974i	−0.838168	+	2.70138i	−0.0244139	−	2.99990i	5.77089	+	0.580682i
277.13	−1.27676	−	0.608187i	−1.55038	−	0.772217i	1.26022	+	1.55302i	2.14506	+	1.23845i	1.50981	+	1.92886i	−2.51672	−	0.816158i	−0.664465	−	2.74927i	1.80736	+	2.39446i	−1.98551	−	2.88580i
277.14	−1.27676	+	0.608187i	1.55038	+	0.772217i	1.26022	−	1.55302i	−2.14506	−	1.23845i	−2.44911	−	0.0430112i	−2.51672	−	0.816158i	−0.664465	+	2.74927i	1.80736	+	2.39446i	3.49193	+	0.276602i
277.15	−1.23730	−	0.684906i	0.549172	+	1.64268i	1.06181	+	1.69486i	−3.35113	−	1.93477i	0.445596	−	2.40862i	−2.41512	+	1.08036i	−0.152946	−	2.82429i	−2.39682	+	1.80423i	2.82120	+	4.68910i
277.16	−1.23730	+	0.684906i	−0.549172	−	1.64268i	1.06181	−	1.69486i	3.35113	+	1.93477i	1.80457	+	1.65636i	−2.41512	+	1.08036i	−0.152946	+	2.82429i	−2.39682	+	1.80423i	−5.47148	−	0.0986814i
277.17	−1.16914	−	0.795682i	0.775861	−	1.54856i	0.733781	+	1.86053i	−0.241073	−	0.139184i	−2.13925	+	1.19315i	−2.22477	−	1.43192i	0.622496	−	2.75908i	−1.79608	−	2.40294i	0.171103	+	0.354543i
277.18	−1.16914	+	0.795682i	−0.775861	+	1.54856i	0.733781	−	1.86053i	0.241073	+	0.139184i	−0.325070	−	2.42782i	−2.22477	−	1.43192i	0.622496	+	2.75908i	−1.79608	−	2.40294i	−0.392595	+	0.0290923i
277.19	−1.15465	−	0.816568i	−1.68787	+	0.388703i	0.666434	+	1.88570i	−1.19505	−	0.689965i	2.26630	+	0.929446i	0.677727	+	2.55748i	0.770303	−	2.72151i	2.69782	−	1.31216i	0.816467	+	1.77251i
277.20	−1.15465	+	0.816568i	1.68787	−	0.388703i	0.666434	−	1.88570i	1.19505	+	0.689965i	−1.63150	+	1.82708i	0.677727	+	2.55748i	0.770303	+	2.72151i	2.69782	−	1.31216i	−1.94327	+	0.179175i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
63.h	even	3	1	inner
504.cq	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	504.2.cq.a	yes	184
7.c	even	3	1		504.2.w.a	✓	184
8.b	even	2	1	inner	504.2.cq.a	yes	184
9.c	even	3	1		504.2.w.a	✓	184
56.p	even	6	1		504.2.w.a	✓	184
63.h	even	3	1	inner	504.2.cq.a	yes	184
72.n	even	6	1		504.2.w.a	✓	184
504.cq	even	6	1	inner	504.2.cq.a	yes	184

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
504.2.w.a	✓	184	7.c	even	3	1
504.2.w.a	✓	184	9.c	even	3	1
504.2.w.a	✓	184	56.p	even	6	1
504.2.w.a	✓	184	72.n	even	6	1
504.2.cq.a	yes	184	1.a	even	1	1	trivial
504.2.cq.a	yes	184	8.b	even	2	1	inner
504.2.cq.a	yes	184	63.h	even	3	1	inner
504.2.cq.a	yes	184	504.cq	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(504, [\chi])\).