Newform orbit 55.4.e.b

• Label: 55.4.e.b
• Level: $55$
• Weight: $4$
• Character orbit: 55.e
• Analytic conductor: $3.245$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	55.e (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.24510505032\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 16 q^{3} + 12 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
32.1	−3.68747	+	3.68747i	−3.73361	+	3.73361i		−	19.1948i	0.748902	−	11.1552i		−	27.5351i	−9.18412	+	9.18412i	41.2806	+	41.2806i		−	0.879688i	38.3730	+	43.8961i
32.2	−3.46644	+	3.46644i	2.24784	−	2.24784i		−	16.0324i	8.23861	+	7.55813i			15.5840i	20.8497	−	20.8497i	27.8439	+	27.8439i			16.8944i	−54.7584	+	2.35882i
32.3	−2.85956	+	2.85956i	3.30070	−	3.30070i		−	8.35418i	−10.4770	+	3.90284i			18.8771i	−15.7496	+	15.7496i	1.01280	+	1.01280i			5.21080i	18.7993	−	41.1201i
32.4	−2.21198	+	2.21198i	−5.48293	+	5.48293i		−	1.78572i	4.40036	+	10.2780i		−	24.2563i	−1.19369	+	1.19369i	−13.7459	−	13.7459i		−	33.1250i	−32.4682	−	13.0012i
32.5	−1.96488	+	1.96488i	4.55271	−	4.55271i			0.278525i	−1.13809	−	11.1223i			17.8910i	12.9680	−	12.9680i	−16.2663	−	16.2663i		−	14.4543i	24.0901	+	19.6177i
32.6	−1.36712	+	1.36712i	−4.36497	+	4.36497i			4.26199i	−9.18141	−	6.37979i		−	11.9348i	17.9353	−	17.9353i	−16.7636	−	16.7636i		−	11.1059i	21.2740	−	3.83013i
32.7	−1.25964	+	1.25964i	−0.519744	+	0.519744i			4.82664i	10.4087	−	4.08166i		−	1.30938i	−17.2517	+	17.2517i	−16.1569	−	16.1569i			26.4597i	−7.96970	+	18.2525i
32.8	1.25964	−	1.25964i	−0.519744	+	0.519744i			4.82664i	10.4087	−	4.08166i			1.30938i	17.2517	−	17.2517i	16.1569	+	16.1569i			26.4597i	7.96970	−	18.2525i
32.9	1.36712	−	1.36712i	−4.36497	+	4.36497i			4.26199i	−9.18141	−	6.37979i			11.9348i	−17.9353	+	17.9353i	16.7636	+	16.7636i		−	11.1059i	−21.2740	+	3.83013i
32.10	1.96488	−	1.96488i	4.55271	−	4.55271i			0.278525i	−1.13809	−	11.1223i		−	17.8910i	−12.9680	+	12.9680i	16.2663	+	16.2663i		−	14.4543i	−24.0901	−	19.6177i
32.11	2.21198	−	2.21198i	−5.48293	+	5.48293i		−	1.78572i	4.40036	+	10.2780i			24.2563i	1.19369	−	1.19369i	13.7459	+	13.7459i		−	33.1250i	32.4682	+	13.0012i
32.12	2.85956	−	2.85956i	3.30070	−	3.30070i		−	8.35418i	−10.4770	+	3.90284i		−	18.8771i	15.7496	−	15.7496i	−1.01280	−	1.01280i			5.21080i	−18.7993	+	41.1201i
32.13	3.46644	−	3.46644i	2.24784	−	2.24784i		−	16.0324i	8.23861	+	7.55813i		−	15.5840i	−20.8497	+	20.8497i	−27.8439	−	27.8439i			16.8944i	54.7584	−	2.35882i
32.14	3.68747	−	3.68747i	−3.73361	+	3.73361i		−	19.1948i	0.748902	−	11.1552i			27.5351i	9.18412	−	9.18412i	−41.2806	−	41.2806i		−	0.879688i	−38.3730	−	43.8961i
43.1	−3.68747	−	3.68747i	−3.73361	−	3.73361i			19.1948i	0.748902	+	11.1552i			27.5351i	−9.18412	−	9.18412i	41.2806	−	41.2806i			0.879688i	38.3730	−	43.8961i
43.2	−3.46644	−	3.46644i	2.24784	+	2.24784i			16.0324i	8.23861	−	7.55813i		−	15.5840i	20.8497	+	20.8497i	27.8439	−	27.8439i		−	16.8944i	−54.7584	−	2.35882i
43.3	−2.85956	−	2.85956i	3.30070	+	3.30070i			8.35418i	−10.4770	−	3.90284i		−	18.8771i	−15.7496	−	15.7496i	1.01280	−	1.01280i		−	5.21080i	18.7993	+	41.1201i
43.4	−2.21198	−	2.21198i	−5.48293	−	5.48293i			1.78572i	4.40036	−	10.2780i			24.2563i	−1.19369	−	1.19369i	−13.7459	+	13.7459i			33.1250i	−32.4682	+	13.0012i
43.5	−1.96488	−	1.96488i	4.55271	+	4.55271i		−	0.278525i	−1.13809	+	11.1223i		−	17.8910i	12.9680	+	12.9680i	−16.2663	+	16.2663i			14.4543i	24.0901	−	19.6177i
43.6	−1.36712	−	1.36712i	−4.36497	−	4.36497i		−	4.26199i	−9.18141	+	6.37979i			11.9348i	17.9353	+	17.9353i	−16.7636	+	16.7636i			11.1059i	21.2740	+	3.83013i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
11.b	odd	2	1	inner
55.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	55.4.e.b	✓	28
5.c	odd	4	1	inner	55.4.e.b	✓	28
11.b	odd	2	1	inner	55.4.e.b	✓	28
55.e	even	4	1	inner	55.4.e.b	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
55.4.e.b	✓	28	1.a	even	1	1	trivial
55.4.e.b	✓	28	5.c	odd	4	1	inner
55.4.e.b	✓	28	11.b	odd	2	1	inner
55.4.e.b	✓	28	55.e	even	4	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^28 + 1764*T2^24 + 1073310*T2^20 + 269436220*T2^16 + 28222096825*T2^12 + 1220411539400*T2^8 + 18805766810000*T2^4 + 91776400000000