Newform orbit 755.2.s.a

• Label: 755.2.s.a
• Level: $755$
• Weight: $2$
• Character orbit: 755.s
• Analytic conductor: $6.029$
• Analytic rank: $0$
• Dimension: $592$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	755.s (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.02870535261\)
Analytic rank:	\(0\)
Dimension:	\(592\)
Relative dimension:	\(74\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 592 * q - 16 * q^2 - 10 * q^3 - 6 * q^5 - 10 * q^7 + 16 * q^8 + 6 * q^10 - 10 * q^13 + 10 * q^15 - 568 * q^16 - 6 * q^17 + 6 * q^18 - 2 * q^20 - 4 * q^21 - 40 * q^22 - 6 * q^25 - 20 * q^26 - 10 * q^27 - 30 * q^28 + 90 * q^30 + 4 * q^31 - 24 * q^32 - 10 * q^35 + 84 * q^36 - 6 * q^37 + 100 * q^38 + 38 * q^40 - 40 * q^41 - 66 * q^42 + 6 * q^43 - 88 * q^45 - 42 * q^47 - 40 * q^48 + 42 * q^50 - 20 * q^51 + 10 * q^52 + 40 * q^53 - 46 * q^55 + 60 * q^56 + 140 * q^57 + 116 * q^58 + 30 * q^60 - 20 * q^61 - 30 * q^62 + 30 * q^63 - 160 * q^65 + 30 * q^67 - 50 * q^68 + 60 * q^70 + 40 * q^71 + 110 * q^72 - 50 * q^73 + 16 * q^76 - 10 * q^77 - 14 * q^78 - 132 * q^80 + 24 * q^81 - 30 * q^82 + 20 * q^83 - 32 * q^85 + 124 * q^86 + 62 * q^88 + 14 * q^90 - 140 * q^91 - 10 * q^93 - 2 * q^95 - 140 * q^96 + 54 * q^97 - 68 * q^98

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
87.1	−1.98460	−	1.98460i	1.94938	+	0.308751i			5.87724i	0.632558	+	2.14473i	−3.25598	−	4.48147i	0.436526	+	0.856730i	7.69475	−	7.69475i	0.851577	+	0.276694i	3.00105	−	5.51179i
87.2	−1.90049	−	1.90049i	−0.266080	−	0.0421429i			5.22374i	1.96893	−	1.05987i	0.425590	+	0.585775i	1.23971	+	2.43307i	6.12669	−	6.12669i	−2.78415	−	0.904624i	−5.75620	−	1.72767i
87.3	−1.88236	−	1.88236i	2.76771	+	0.438363i			5.08657i	−1.66401	−	1.49367i	−4.38468	−	6.03500i	0.0830858	+	0.163065i	5.81004	−	5.81004i	4.61491	+	1.49948i	0.320642	+	5.94391i
87.4	−1.86754	−	1.86754i	−2.90481	−	0.460077i			4.97539i	−0.219116	−	2.22531i	4.56563	+	6.28405i	−1.28090	−	2.51391i	5.55664	−	5.55664i	5.37309	+	1.74582i	−3.74663	+	4.56505i
87.5	−1.83343	−	1.83343i	−1.82239	−	0.288637i			4.72297i	−1.95127	+	1.09204i	2.81203	+	3.87042i	−0.491881	−	0.965371i	4.99238	−	4.99238i	0.384607	+	0.124966i	5.57971	+	1.57534i
87.6	−1.72753	−	1.72753i	−1.54662	−	0.244961i			3.96870i	2.12654	+	0.691254i	2.24866	+	3.09501i	−2.06112	−	4.04517i	3.40097	−	3.40097i	−0.521133	−	0.169326i	−2.47949	−	4.86781i
87.7	−1.70788	−	1.70788i	1.13308	+	0.179462i			3.83368i	1.84924	−	1.25711i	−1.62866	−	2.24166i	−0.343685	−	0.674520i	3.13170	−	3.13170i	−1.60151	−	0.520361i	−5.30525	−	1.01128i
87.8	−1.68678	−	1.68678i	−1.20182	−	0.190350i			3.69042i	−1.07480	−	1.96082i	1.70613	+	2.34828i	1.82377	+	3.57935i	2.85136	−	2.85136i	−1.44502	−	0.469516i	−1.49452	+	5.12040i
87.9	−1.67245	−	1.67245i	−2.94102	−	0.465811i			3.59418i	0.548171	+	2.16783i	4.13966	+	5.69775i	1.39664	+	2.74106i	2.66619	−	2.66619i	5.57942	+	1.81286i	2.70881	−	4.54239i
87.10	−1.66721	−	1.66721i	0.738036	+	0.116893i			3.55918i	−2.08198	−	0.815693i	−1.03557	−	1.42535i	−1.54098	−	3.02434i	2.59948	−	2.59948i	−2.32214	−	0.754508i	2.11117	+	4.83103i
87.11	−1.55951	−	1.55951i	1.45725	+	0.230805i			2.86411i	0.758601	+	2.10346i	−1.91264	−	2.63253i	−1.74795	−	3.43054i	1.34759	−	1.34759i	−0.782868	−	0.254369i	2.09731	−	4.46339i
87.12	−1.49425	−	1.49425i	0.279235	+	0.0442265i			2.46554i	−0.150120	+	2.23102i	−0.351161	−	0.483331i	2.01479	+	3.95425i	0.695639	−	0.695639i	−2.77715	−	0.902352i	3.55801	−	3.10938i
87.13	−1.47447	−	1.47447i	2.24041	+	0.354846i			2.34813i	0.669715	−	2.13342i	−2.78020	−	3.82662i	−0.0691630	−	0.135740i	0.513301	−	0.513301i	2.04034	+	0.662946i	−4.13314	+	2.15819i
87.14	−1.36078	−	1.36078i	3.06174	+	0.484932i			1.70344i	2.21188	+	0.327992i	−3.50647	−	4.82624i	1.82923	+	3.59007i	−0.403546	+	0.403546i	6.28591	+	2.04241i	−2.56356	−	3.45621i
87.15	−1.33088	−	1.33088i	3.12646	+	0.495183i			1.54247i	−1.28633	+	1.82903i	−3.50191	−	4.81997i	−0.475703	−	0.933619i	−0.608916	+	0.608916i	6.67640	+	2.16929i	4.14617	−	0.722262i
87.16	−1.30770	−	1.30770i	−1.19019	−	0.188508i			1.42018i	1.75507	+	1.38554i	1.30991	+	1.80293i	0.323588	+	0.635078i	−0.758227	+	0.758227i	−1.47215	−	0.478331i	−0.483229	−	4.10700i
87.17	−1.21987	−	1.21987i	−2.81696	−	0.446163i			0.976151i	2.00515	−	0.989624i	2.89206	+	3.98058i	0.292741	+	0.574536i	−1.24896	+	1.24896i	4.88303	+	1.58659i	−3.65323	−	1.23881i
87.18	−1.18786	−	1.18786i	−2.00510	−	0.317577i			0.822026i	−1.82901	+	1.28635i	2.00454	+	2.75902i	−0.911490	−	1.78890i	−1.39927	+	1.39927i	1.06640	+	0.346495i	3.70062	+	0.644603i
87.19	−1.12275	−	1.12275i	1.37132	+	0.217196i			0.521121i	−2.17967	−	0.499056i	−1.29579	−	1.78350i	1.36426	+	2.67751i	−1.66041	+	1.66041i	−1.01983	−	0.331362i	1.88690	+	3.00753i
87.20	−1.09994	−	1.09994i	−1.73160	−	0.274259i			0.419746i	−2.19515	−	0.425836i	1.60300	+	2.20633i	0.993637	+	1.95012i	−1.73819	+	1.73819i	0.0700639	+	0.0227651i	1.94614	+	2.88293i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
151.f	odd	10	1	inner
755.s	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	755.2.s.a	✓	592
5.c	odd	4	1	inner	755.2.s.a	✓	592
151.f	odd	10	1	inner	755.2.s.a	✓	592
755.s	even	20	1	inner	755.2.s.a	✓	592

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
755.2.s.a	✓	592	1.a	even	1	1	trivial
755.2.s.a	✓	592	5.c	odd	4	1	inner
755.2.s.a	✓	592	151.f	odd	10	1	inner
755.2.s.a	✓	592	755.s	even	20	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(755, [\chi])\).