Newform orbit 63.4.s.a

• Label: 63.4.s.a
• Level: $63$
• Weight: $4$
• Character orbit: 63.s
• Analytic conductor: $3.717$
• Analytic rank: $0$
• Dimension: $44$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.71712033036\)
Analytic rank:	\(0\)
Dimension:	\(44\)
Relative dimension:	\(22\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
47.1	−4.53659	+	2.61920i	2.85276	+	4.34301i	9.72046	−	16.8363i	−12.2114			−24.3171	−	12.2305i	−10.8477	−	15.0109i			59.9322i	−10.7235	+	24.7791i	55.3983	−	31.9842i
47.2	−4.33849	+	2.50483i	−5.18070	+	0.400483i	8.54831	−	14.8061i	18.5684			21.4732	−	14.7142i	−17.9322	−	4.62983i			45.5709i	26.6792	−	4.14956i	−80.5586	+	46.5105i
47.3	−4.26829	+	2.46430i	−1.44219	−	4.99200i	8.14552	−	14.1085i	−9.24869			18.4575	+	17.7533i	17.8986	+	4.75801i			40.8632i	−22.8402	+	14.3988i	39.4761	−	22.7915i
47.4	−3.22249	+	1.86051i	4.92551	−	1.65511i	2.92296	−	5.06272i	2.66012			−12.7931	+	14.4975i	9.53109	−	15.8795i		−	8.01534i	21.5212	−	16.3045i	−8.57221	+	4.94917i
47.5	−3.16085	+	1.82492i	−3.78544	+	3.55956i	2.66064	−	4.60836i	−12.2314			5.46929	−	18.1593i	4.78838	+	17.8905i		−	9.77690i	1.65907	−	26.9490i	38.6615	−	22.3212i
47.6	−3.00186	+	1.73312i	2.62001	+	4.48727i	2.00744	−	3.47699i	18.0540			−15.6419	−	8.92935i	12.2090	+	13.9263i		−	13.8134i	−13.2711	+	23.5133i	−54.1956	+	31.2898i
47.7	−2.65116	+	1.53065i	1.23858	−	5.04638i	0.685763	−	1.18778i	5.50223			4.44054	+	15.2746i	−18.4916	+	1.02989i		−	20.2917i	−23.9318	−	12.5007i	−14.5873	+	8.42197i
47.8	−1.59189	+	0.919076i	−5.10006	−	0.994690i	−2.31060	+	4.00207i	0.414554			9.03291	−	3.10391i	12.7471	−	13.4355i		−	23.1997i	25.0212	+	10.1460i	−0.659923	+	0.381007i
47.9	−1.54833	+	0.893930i	5.18374	+	0.358957i	−2.40178	+	4.16000i	−16.9434			−8.34703	+	4.07812i	−9.83512	+	15.6930i		−	22.8910i	26.7423	+	3.72148i	26.2340	−	15.1462i
47.10	−0.998155	+	0.576285i	−1.29916	+	5.03112i	−3.33579	+	5.77776i	0.274718			−1.60260	−	5.77053i	−9.15344	−	16.1001i		−	16.9100i	−23.6244	−	13.0725i	−0.274212	+	0.158316i
47.11	−0.223110	+	0.128812i	−3.39738	−	3.93164i	−3.96681	+	6.87072i	6.38772			1.26443	+	0.439563i	−1.54394	+	18.4558i		−	4.10490i	−3.91563	+	26.7146i	−1.42516	+	0.822818i
47.12	0.647627	−	0.373907i	4.16400	−	3.10824i	−3.72039	+	6.44390i	8.70220			1.53452	−	3.56993i	18.2993	+	2.85258i			11.5468i	7.67775	−	25.8854i	5.63577	−	3.25382i
47.13	0.725355	−	0.418784i	0.141982	−	5.19421i	−3.64924	+	6.32067i	−21.9169			−2.07226	−	3.82711i	2.19637	−	18.3896i			12.8135i	−26.9597	−	1.47497i	−15.8975	+	9.17842i
47.14	0.958607	−	0.553452i	4.58314	+	2.44844i	−3.38738	+	5.86712i	12.4738			5.74852	−	0.189454i	−18.2811	−	2.96677i			16.3542i	15.0103	+	22.4431i	11.9574	−	6.90363i
47.15	1.57448	−	0.909026i	0.874715	+	5.12200i	−2.34735	+	4.06572i	−10.3247			6.03325	+	7.26934i	15.1453	+	10.6593i			23.0796i	−25.4697	+	8.96058i	−16.2560	+	9.38543i
47.16	2.09278	−	1.20827i	−5.12336	+	0.866692i	−1.08019	+	1.87094i	−10.7193			−9.67487	+	8.00418i	−17.6173	+	5.71220i			24.5529i	25.4977	−	8.88075i	−22.4331	+	12.9518i
47.17	2.52419	−	1.45734i	−4.29460	+	2.92513i	0.247680	−	0.428994i	17.2113			−6.57748	+	13.6423i	17.7231	−	5.37495i			21.8736i	9.88725	−	25.1245i	43.4446	−	25.0828i
47.18	3.22215	−	1.86031i	−1.86223	−	4.85099i	2.92152	−	5.06021i	13.6667			−15.0248	−	12.1663i	−10.0995	−	15.5242i			8.02526i	−20.0642	+	18.0673i	44.0363	−	25.4243i
47.19	3.55689	−	2.05357i	4.91877	+	1.67502i	4.43430	−	7.68044i	−7.61183			20.9353	−	4.14318i	4.76690	−	17.8963i		−	3.56749i	21.3886	+	16.4781i	−27.0744	+	15.6314i
47.20	3.68213	−	2.12588i	3.24389	−	4.05921i	5.03872	−	8.72732i	−2.97507			3.31505	−	21.8426i	−4.05014	+	18.0720i		−	8.83278i	−5.95432	−	26.3353i	−10.9546	+	6.32464i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
63.s	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	63.4.s.a	yes	44
3.b	odd	2	1		189.4.s.a		44
7.d	odd	6	1		63.4.i.a	✓	44
9.c	even	3	1		189.4.i.a		44
9.d	odd	6	1		63.4.i.a	✓	44
21.g	even	6	1		189.4.i.a		44
63.k	odd	6	1		189.4.s.a		44
63.s	even	6	1	inner	63.4.s.a	yes	44

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
63.4.i.a	✓	44	7.d	odd	6	1
63.4.i.a	✓	44	9.d	odd	6	1
63.4.s.a	yes	44	1.a	even	1	1	trivial
63.4.s.a	yes	44	63.s	even	6	1	inner
189.4.i.a		44	9.c	even	3	1
189.4.i.a		44	21.g	even	6	1
189.4.s.a		44	3.b	odd	2	1
189.4.s.a		44	63.k	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(63, [\chi])\).