Newform orbit 31.6.c.a

• Label: 31.6.c.a
• Level: $31$
• Weight: $6$
• Character orbit: 31.c
• Analytic conductor: $4.972$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	31.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.97189841420\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{2} + 10 q^{3} + 336 q^{4} + 28 q^{5} + 72 q^{6} - 134 q^{7} - 804 q^{8} - 668 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−10.6675			−9.81192	+	16.9947i	81.7957			38.7555	+	67.1265i	104.669	−	181.291i	−59.2389	+	102.605i	−531.196			−71.0474	−	123.058i	−413.425	−	716.073i
5.2	−9.13733			10.6162	−	18.3878i	51.4907			15.6182	+	27.0515i	−97.0036	+	168.015i	58.3844	−	101.125i	−178.093			−103.907	−	179.973i	−142.708	−	247.178i
5.3	−8.02148			−0.0464880	+	0.0805196i	32.3442			−36.4382	−	63.1128i	0.372903	−	0.645886i	−40.4814	+	70.1158i	−2.76070			121.496	+	210.437i	292.288	+	506.258i
5.4	−4.29567			−10.9984	+	19.0497i	−13.5472			−1.64079	−	2.84193i	47.2454	−	81.8313i	35.2060	−	60.9786i	195.656			−120.428	−	208.587i	7.04829	+	12.2080i
5.5	−3.54056			3.25294	−	5.63426i	−19.4645			28.7785	+	49.8458i	−11.5172	+	19.9484i	37.7117	−	65.3186i	182.213			100.337	+	173.788i	−101.892	−	176.482i
5.6	−1.70741			12.7319	−	22.0522i	−29.0848			−18.7233	−	32.4296i	−21.7385	+	37.6521i	−98.1990	+	170.086i	104.297			−202.700	−	351.087i	31.9682	+	55.3706i
5.7	2.31759			−2.39188	+	4.14286i	−26.6288			25.7398	+	44.5826i	−5.54340	+	9.60145i	−77.7552	+	134.676i	−135.877			110.058	+	190.626i	59.6542	+	103.324i
5.8	2.80839			1.76382	−	3.05503i	−24.1129			−42.4669	−	73.5549i	4.95350	−	8.57972i	87.7771	−	152.034i	−157.587			115.278	+	199.667i	−119.264	−	206.571i
5.9	5.24194			−12.7901	+	22.1531i	−4.52208			−18.8032	−	32.5680i	−67.0450	+	116.125i	−37.5829	+	65.0956i	−191.446			−205.674	−	356.238i	−98.5650	−	170.720i
5.10	6.13290			12.2809	−	21.2712i	5.61246			28.8125	+	49.9047i	75.3176	−	130.454i	56.7385	−	98.2740i	−161.832			−180.142	−	312.015i	176.704	+	306.061i
5.11	9.21647			−5.72200	+	9.91079i	52.9433			23.9452	+	41.4743i	−52.7366	+	91.3425i	50.4934	−	87.4572i	193.023			56.0175	+	97.0251i	220.690	+	382.247i
5.12	9.65266			6.11503	−	10.5915i	61.1738			−29.5773	−	51.2294i	59.0262	−	102.236i	−80.0536	+	138.657i	281.605			46.7129	+	80.9092i	−285.500	−	494.500i
25.1	−10.6675			−9.81192	−	16.9947i	81.7957			38.7555	−	67.1265i	104.669	+	181.291i	−59.2389	−	102.605i	−531.196			−71.0474	+	123.058i	−413.425	+	716.073i
25.2	−9.13733			10.6162	+	18.3878i	51.4907			15.6182	−	27.0515i	−97.0036	−	168.015i	58.3844	+	101.125i	−178.093			−103.907	+	179.973i	−142.708	+	247.178i
25.3	−8.02148			−0.0464880	−	0.0805196i	32.3442			−36.4382	+	63.1128i	0.372903	+	0.645886i	−40.4814	−	70.1158i	−2.76070			121.496	−	210.437i	292.288	−	506.258i
25.4	−4.29567			−10.9984	−	19.0497i	−13.5472			−1.64079	+	2.84193i	47.2454	+	81.8313i	35.2060	+	60.9786i	195.656			−120.428	+	208.587i	7.04829	−	12.2080i
25.5	−3.54056			3.25294	+	5.63426i	−19.4645			28.7785	−	49.8458i	−11.5172	−	19.9484i	37.7117	+	65.3186i	182.213			100.337	−	173.788i	−101.892	+	176.482i
25.6	−1.70741			12.7319	+	22.0522i	−29.0848			−18.7233	+	32.4296i	−21.7385	−	37.6521i	−98.1990	−	170.086i	104.297			−202.700	+	351.087i	31.9682	−	55.3706i
25.7	2.31759			−2.39188	−	4.14286i	−26.6288			25.7398	−	44.5826i	−5.54340	−	9.60145i	−77.7552	−	134.676i	−135.877			110.058	−	190.626i	59.6542	−	103.324i
25.8	2.80839			1.76382	+	3.05503i	−24.1129			−42.4669	+	73.5549i	4.95350	+	8.57972i	87.7771	+	152.034i	−157.587			115.278	−	199.667i	−119.264	+	206.571i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
31.c	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	31.6.c.a	✓	24
31.c	even	3	1	inner	31.6.c.a	✓	24
31.c	even	3	1		961.6.a.e		12
31.e	odd	6	1		961.6.a.f		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
31.6.c.a	✓	24	1.a	even	1	1	trivial
31.6.c.a	✓	24	31.c	even	3	1	inner
961.6.a.e		12	31.c	even	3	1
961.6.a.f		12	31.e	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(31, [\chi])\).