Newform orbit 805.2.c.c

• Label: 805.2.c.c
• Level: $805$
• Weight: $2$
• Character orbit: 805.c
• Analytic conductor: $6.428$
• Analytic rank: $0$
• Dimension: $42$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.42795736271\)
Analytic rank:	\(0\)
Dimension:	\(42\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 42 q - 60 q^{4} + 2 q^{5} + 12 q^{6} - 60 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
484.1		−	2.80022i		−	0.208644i	−5.84124			−1.70159	−	1.45072i	−0.584249					1.00000i			10.7563i	2.95647			−4.06234	+	4.76483i
484.2		−	2.72900i		−	3.06108i	−5.44746			−2.23566	+	0.0429229i	−8.35371				−	1.00000i			9.40815i	−6.37023			0.117137	+	6.10111i
484.3		−	2.70441i			1.97894i	−5.31383			0.525494	+	2.17344i	5.35185				−	1.00000i			8.96197i	−0.916187			5.87788	−	1.42115i
484.4		−	2.68001i			3.08395i	−5.18247			1.08626	−	1.95449i	8.26504					1.00000i			8.52906i	−6.51078			−5.23807	−	2.91118i
484.5		−	2.57149i			0.285863i	−4.61257			1.95531	−	1.08478i	0.735095				−	1.00000i			6.71821i	2.91828			−2.78950	−	5.02807i
484.6		−	2.38755i		−	1.09554i	−3.70041			2.13213	+	0.673804i	−2.61567					1.00000i			4.05982i	1.79978			1.60874	−	5.09058i
484.7		−	2.35921i			2.50751i	−3.56589			−2.09438	−	0.783299i	5.91575				−	1.00000i			3.69426i	−3.28760			−1.84797	+	4.94110i
484.8		−	2.20248i			2.83822i	−2.85093			−0.287811	+	2.21747i	6.25112					1.00000i			1.87416i	−5.05547			4.88394	+	0.633899i
484.9		−	2.11197i		−	1.59044i	−2.46043			−1.77982	+	1.35361i	−3.35897				−	1.00000i			0.972410i	0.470497			2.85878	+	3.75893i
484.10		−	1.67541i		−	3.24787i	−0.806990			−0.276266	+	2.21894i	−5.44150					1.00000i		−	1.99878i	−7.54864			3.71762	+	0.462857i
484.11		−	1.61751i		−	2.88096i	−0.616354			2.14065	+	0.646219i	−4.65999				−	1.00000i		−	2.23807i	−5.29992			1.04527	−	3.46254i
484.12		−	1.53505i			0.943091i	−0.356385			0.00201580	−	2.23607i	1.44769					1.00000i		−	2.52303i	2.11058			−3.43248	−	0.00309436i
484.13		−	1.50084i		−	0.816695i	−0.252529			2.06282	−	0.863005i	−1.22573				−	1.00000i		−	2.62268i	2.33301			−1.29523	−	3.09597i
484.14		−	1.30923i			2.43985i	0.285909			0.245062	−	2.22260i	3.19433				−	1.00000i		−	2.99279i	−2.95286			−2.90990	−	0.320843i
484.15		−	1.22234i		−	1.28664i	0.505878			1.74857	−	1.39374i	−1.57271					1.00000i		−	3.06304i	1.34457			−1.70363	−	2.13735i
484.16		−	0.817573i			1.89500i	1.33157			−1.04173	+	1.97858i	1.54930				−	1.00000i		−	2.72381i	−0.591014			1.61764	+	0.851693i
484.17		−	0.685218i			1.12744i	1.53048			−2.23604	−	0.0108956i	0.772540					1.00000i		−	2.41915i	1.72889			−0.00746587	+	1.53218i
484.18		−	0.556064i			2.94180i	1.69079			1.39046	+	1.75118i	1.63583					1.00000i		−	2.05232i	−5.65418			0.973767	−	0.773184i
484.19		−	0.475047i		−	0.568069i	1.77433			−0.0751241	−	2.23481i	−0.269859				−	1.00000i		−	1.79298i	2.67730			−1.06164	+	0.0356875i
484.20		−	0.294301i		−	3.07644i	1.91339			1.51307	−	1.64640i	−0.905400					1.00000i		−	1.15171i	−6.46449			−0.484536	−	0.445298i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	805.2.c.c	✓	42
5.b	even	2	1	inner	805.2.c.c	✓	42
5.c	odd	4	1		4025.2.a.bd		21
5.c	odd	4	1		4025.2.a.be		21

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
805.2.c.c	✓	42	1.a	even	1	1	trivial
805.2.c.c	✓	42	5.b	even	2	1	inner
4025.2.a.bd		21	5.c	odd	4	1
4025.2.a.be		21	5.c	odd	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^42 + 72*T2^40 + 2390*T2^38 + 48524*T2^36 + 674123*T2^34 + 6793094*T2^32 + 51360330*T2^30 + 297309418*T2^28 + 1333001717*T2^26 + 4653667576*T2^24 + 12653230895*T2^22 + 26677794870*T2^20 + 43224551182*T2^18 + 53067196190*T2^16 + 48389004712*T2^14 + 31892543150*T2^12 + 14654987288*T2^10 + 4475442828*T2^8 + 849434761*T2^6 + 90209334*T2^4 + 4417689*T2^2 + 65536