Newform orbit 79.11.b.c

• Label: 79.11.b.c
• Level: $79$
• Weight: $11$
• Character orbit: 79.b
• Analytic conductor: $50.193$
• Analytic rank: $0$
• Dimension: $60$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	79.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(50.1932229612\)
Analytic rank:	\(0\)
Dimension:	\(60\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 60 q + 20 q^{2} + 26656 q^{4} - 2 q^{5} - 28472 q^{8} - 1416490 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
78.1	−59.2591				−	350.719i	2487.64			3184.00					20783.3i			2912.67i	−86733.9			−63954.8			−188681.
78.2	−59.2591					350.719i	2487.64			3184.00				−	20783.3i		−	2912.67i	−86733.9			−63954.8			−188681.
78.3	−56.7215				−	213.412i	2193.33			−3061.46					12105.0i		−	20440.0i	−66326.2			13504.3			173651.
78.4	−56.7215					213.412i	2193.33			−3061.46				−	12105.0i			20440.0i	−66326.2			13504.3			173651.
78.5	−54.0718				−	4.33927i	1899.76			4231.68					234.632i			29082.5i	−47354.0			59030.2			−228815.
78.6	−54.0718					4.33927i	1899.76			4231.68				−	234.632i		−	29082.5i	−47354.0			59030.2			−228815.
78.7	−50.5490				−	436.448i	1531.20			−1660.48					22062.0i			10596.7i	−25638.5			−131438.			83935.8
78.8	−50.5490					436.448i	1531.20			−1660.48				−	22062.0i		−	10596.7i	−25638.5			−131438.			83935.8
78.9	−48.1637				−	213.997i	1295.74			−4201.96					10306.9i			17054.1i	−13088.0			13254.2			202382.
78.10	−48.1637					213.997i	1295.74			−4201.96				−	10306.9i		−	17054.1i	−13088.0			13254.2			202382.
78.11	−44.8104				−	181.872i	983.975			2327.25					8149.76i		−	4229.66i	1793.53			25971.6			−104285.
78.12	−44.8104					181.872i	983.975			2327.25				−	8149.76i			4229.66i	1793.53			25971.6			−104285.
78.13	−37.8705				−	76.7639i	410.172			886.843					2907.08i			17801.0i	23245.9			53156.3			−33585.2
78.14	−37.8705					76.7639i	410.172			886.843				−	2907.08i		−	17801.0i	23245.9			53156.3			−33585.2
78.15	−34.4717				−	394.036i	164.295			801.475					13583.1i		−	28217.1i	29635.5			−96215.0			−27628.2
78.16	−34.4717					394.036i	164.295			801.475				−	13583.1i			28217.1i	29635.5			−96215.0			−27628.2
78.17	−29.9403				−	370.100i	−127.577			6141.63					11080.9i			6073.10i	34478.6			−77924.8			−183883.
78.18	−29.9403					370.100i	−127.577			6141.63				−	11080.9i		−	6073.10i	34478.6			−77924.8			−183883.
78.19	−28.8439				−	166.061i	−192.030			−4935.71					4789.84i		−	22069.6i	35075.0			31472.8			142365.
78.20	−28.8439					166.061i	−192.030			−4935.71				−	4789.84i			22069.6i	35075.0			31472.8			142365.

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	79.11.b.c	✓	60
79.b	odd	2	1	inner	79.11.b.c	✓	60

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
79.11.b.c	✓	60	1.a	even	1	1	trivial
79.11.b.c	✓	60	79.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^30 - 10*T2^29 - 21974*T2^28 + 217992*T2^27 + 215020449*T2^26 - 2123064652*T2^25 - 1237217773030*T2^24 + 12176560579208*T2^23 + 4655962218227388*T2^22 - 45676934422148208*T2^21 - 12058680088239894056*T2^20 + 117803858269761427936*T2^19 + 22024882925422083021056*T2^18 - 213915375714019012485120*T2^17 - 28594960090513431820537856*T2^16 + 275586257264430876442042368*T2^15 + 26256739223642620390409797632*T2^14 - 250545166915652634437325422592*T2^13 - 16748131585554939123442631835648*T2^12 + 157696789793781851812032581468160*T2^11 + 7171390109809749016377280285376512*T2^10 - 66159392579035468686157823780847616*T2^9 - 1942147006056003830255011722646519808*T2^8 + 17262803506416661927232188060073459712*T2^7 + 298440021856064917238885073768406843392*T2^6 - 2451942065659409886729391975371945017344*T2^5 - 20600343702232477842273353007912695365632*T2^4 + 137944748266096904323544254393998332919808*T2^3 + 284160144793192885481338570642797629538304*T2^2 - 394693931616277863108095049667732750467072*T2 + 9651865889252974031557685370289546854400