Newform orbit 103.5.d.a

• Label: 103.5.d.a
• Level: $103$
• Weight: $5$
• Character orbit: 103.d
• Analytic conductor: $10.647$
• Analytic rank: $0$
• Dimension: $68$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 103 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	103.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.6471061976\)
Analytic rank:	\(0\)
Dimension:	\(68\)
Relative dimension:	\(34\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 68 q - q^{2} - 273 q^{4} - 3 q^{5} + 141 q^{6} + 69 q^{7} - 62 q^{8} - 1688 q^{9}+O(q^{10}) \)

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	−3.74651	+	6.48914i			7.64489i	−20.0727	−	34.7669i	38.1766	−	22.0413i	−49.6088	−	28.6416i	4.69709	+	8.13559i	180.921			22.5557					330.312i
47.2	−3.69468	+	6.39937i		−	12.0077i	−19.3013	−	33.4309i	−36.4180	+	21.0259i	76.8420	+	44.3648i	−43.2359	−	74.8867i	167.019			−63.1859				−	310.737i
47.3	−3.54775	+	6.14488i		−	5.82509i	−17.1731	−	29.7446i	−5.56266	+	3.21160i	35.7945	+	20.6660i	39.5088	+	68.4313i	130.175			47.0683				−	45.5758i
47.4	−3.50556	+	6.07181i			11.1230i	−16.5780	−	28.7139i	−16.0973	+	9.29379i	−67.5370	−	38.9925i	−12.8103	−	22.1881i	120.282			−42.7219				−	130.320i
47.5	−3.37632	+	5.84797i		−	16.1447i	−14.7991	−	25.6329i	41.5202	−	23.9717i	94.4134	+	54.5096i	−15.5480	−	26.9300i	91.8243			−179.650					323.745i
47.6	−2.86577	+	4.96365i		−	0.378281i	−8.42524	−	14.5929i	4.35841	−	2.51633i	1.87765	+	1.08406i	−16.6755	−	28.8828i	4.87452			80.8569					28.8448i
47.7	−2.43361	+	4.21514i		−	13.5188i	−3.84494	−	6.65963i	−8.10666	+	4.68038i	56.9837	+	32.8995i	22.3886	+	38.7781i	−40.4473			−101.758				−	45.5609i
47.8	−2.41082	+	4.17566i			8.31214i	−3.62408	−	6.27708i	−34.8108	+	20.0980i	−34.7087	−	20.0391i	36.2467	+	62.7811i	−42.1982			11.9083				−	193.810i
47.9	−2.24126	+	3.88198i		−	5.27644i	−2.04650	−	3.54464i	17.1109	−	9.87896i	20.4830	+	11.8259i	−22.6160	−	39.1721i	−53.3734			53.1592					88.5653i
47.10	−2.19235	+	3.79725i			15.4323i	−1.61276	−	2.79339i	20.7272	−	11.9669i	−58.6003	−	33.8329i	8.18049	+	14.1690i	−56.0121			−157.155					104.942i
47.11	−1.76621	+	3.05916i			5.24443i	1.76101	+	3.05015i	26.9955	−	15.5859i	−16.0436	−	9.26276i	28.6629	+	49.6455i	−68.9599			53.4960					110.112i
47.12	−1.33023	+	2.30403i			13.1193i	4.46095	+	7.72660i	−10.2236	+	5.90257i	−30.2272	−	17.4517i	−37.8292	−	65.5221i	−66.3040			−91.1149				−	31.4072i
47.13	−1.32492	+	2.29483i		−	2.99770i	4.48917	+	7.77547i	−40.2961	+	23.2650i	6.87920	+	3.97171i	−15.7118	−	27.2137i	−66.1887			72.0138				−	123.297i
47.14	−1.32311	+	2.29170i		−	12.0355i	4.49875	+	7.79206i	−11.4020	+	6.58293i	27.5818	+	15.9243i	4.63537	+	8.02870i	−66.1490			−63.8537				−	34.8398i
47.15	−0.500215	+	0.866399i		−	10.6042i	7.49957	+	12.9896i	35.7814	−	20.6584i	9.18745	+	5.30438i	28.3607	+	49.1222i	−31.0125			−31.4487					41.3346i
47.16	−0.272828	+	0.472553i			6.83193i	7.85113	+	13.5986i	−6.74355	+	3.89339i	−3.22845	−	1.86394i	25.6804	+	44.4798i	−17.2986			34.3247				−	4.24891i
47.17	−0.138835	+	0.240469i			2.78774i	7.96145	+	13.7896i	31.5616	−	18.2221i	−0.670364	−	0.387035i	−40.4270	−	70.0216i	−8.86401			73.2285					10.1194i
47.18	−0.111356	+	0.192874i			1.46551i	7.97520	+	13.8135i	−2.01770	+	1.16492i	−0.282659	−	0.163194i	7.25550	+	12.5669i	−7.11573			78.8523				−	0.518882i
47.19	0.250462	−	0.433813i		−	15.8627i	7.87454	+	13.6391i	0.848199	−	0.489708i	−6.88145	−	3.97301i	−37.0776	−	64.2202i	15.9039			−170.625				−	0.490613i
47.20	0.651598	−	1.12860i			16.6811i	7.15084	+	12.3856i	−25.7520	+	14.8679i	18.8263	+	10.8693i	19.7172	+	34.1512i	39.4890			−197.257					38.7516i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
103.d	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	103.5.d.a	✓	68
103.d	odd	6	1	inner	103.5.d.a	✓	68

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
103.5.d.a	✓	68	1.a	even	1	1	trivial
103.5.d.a	✓	68	103.d	odd	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(103, [\chi])\).