Newform orbit 177.5.c.a

• Label: 177.5.c.a
• Level: $177$
• Weight: $5$
• Character orbit: 177.c
• Analytic conductor: $18.296$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.2964834658\)
Analytic rank:	\(0\)
Dimension:	\(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 320 q^{4} + 80 q^{7} + 1080 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
58.1		−	7.81880i	5.19615			−45.1337			21.3172				−	40.6277i	−30.7266					227.790i	27.0000				−	166.675i
58.2		−	7.77798i	−5.19615			−44.4970			28.5836					40.4156i	72.7001					221.650i	27.0000				−	222.323i
58.3		−	7.65331i	−5.19615			−42.5731			−38.1687					39.7678i	−35.1454					203.372i	27.0000					292.117i
58.4		−	6.76718i	5.19615			−29.7948			6.77685				−	35.1633i	45.8846					93.3518i	27.0000				−	45.8602i
58.5		−	6.70986i	5.19615			−29.0222			−41.0870				−	34.8655i	−6.70931					87.3773i	27.0000					275.688i
58.6		−	6.10324i	−5.19615			−21.2495			−12.8499					31.7133i	4.61608					32.0389i	27.0000					78.4262i
58.7		−	5.77154i	−5.19615			−17.3107			34.3452					29.9898i	−39.2727					7.56484i	27.0000				−	198.225i
58.8		−	4.96663i	5.19615			−8.66741			41.3974				−	25.8074i	1.08721				−	36.4182i	27.0000				−	205.606i
58.9		−	4.85825i	−5.19615			−7.60257			−12.5087					25.2442i	50.4755				−	40.7968i	27.0000					60.7705i
58.10		−	4.64719i	5.19615			−5.59638			−0.691812				−	24.1475i	−76.1022				−	48.3476i	27.0000					3.21498i
58.11		−	4.10319i	−5.19615			−0.836195			−39.6276					21.3208i	−85.8400				−	62.2200i	27.0000					162.600i
58.12		−	4.05068i	−5.19615			−0.408022			−16.4107					21.0480i	47.3137				−	63.1581i	27.0000					66.4744i
58.13		−	3.44422i	5.19615			4.13738			−16.2205				−	17.8967i	92.6602				−	69.3575i	27.0000					55.8670i
58.14		−	2.43119i	5.19615			10.0893			25.9319				−	12.6328i	−17.4595				−	63.4281i	27.0000				−	63.0454i
58.15		−	2.33963i	−5.19615			10.5261			30.0439					12.1571i	−41.7287				−	62.0613i	27.0000				−	70.2916i
58.16		−	2.31914i	5.19615			10.6216			−38.6371				−	12.0506i	9.48964				−	61.7392i	27.0000					89.6048i
58.17		−	2.15560i	−5.19615			11.3534			30.9385					11.2008i	73.3307				−	58.9629i	27.0000				−	66.6909i
58.18		−	1.07792i	5.19615			14.8381			26.1400				−	5.60104i	49.1298				−	33.2410i	27.0000				−	28.1769i
58.19		−	0.850217i	−5.19615			15.2771			−11.2738					4.41785i	−26.4494				−	26.5923i	27.0000					9.58520i
58.20		−	0.389117i	5.19615			15.8486			−17.9988				−	2.02191i	−47.2538				−	12.3928i	27.0000					7.00365i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	177.5.c.a	✓	40
3.b	odd	2	1		531.5.c.d		40
59.b	odd	2	1	inner	177.5.c.a	✓	40
177.d	even	2	1		531.5.c.d		40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
177.5.c.a	✓	40	1.a	even	1	1	trivial
177.5.c.a	✓	40	59.b	odd	2	1	inner
531.5.c.d		40	3.b	odd	2	1
531.5.c.d		40	177.d	even	2	1

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(177, [\chi])\).