Newform orbit 77.5.c.a

• Label: 77.5.c.a
• Level: $77$
• Weight: $5$
• Character orbit: 77.c
• Analytic conductor: $7.959$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	77.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.95948715746\)
Analytic rank:	\(0\)
Dimension:	\(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 6 q^{3} - 198 q^{4} + 6 q^{5} + 982 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
43.1		−	7.50070i	12.9809			−40.2604			45.7388				−	97.3660i		−	18.5203i			181.970i	87.5044				−	343.073i
43.2		−	7.10705i	−11.8255			−34.5101			2.92518					84.0441i			18.5203i			131.553i	58.8413				−	20.7894i
43.3		−	6.94342i	−1.45445			−32.2111			−12.5619					10.0988i		−	18.5203i			112.560i	−78.8846					87.2222i
43.4		−	6.92947i	9.37985			−32.0176			−36.0526				−	64.9974i			18.5203i			110.993i	6.98151					249.826i
43.5		−	4.80284i	−16.4118			−7.06726			−41.5497					78.8230i		−	18.5203i		−	42.9025i	188.346					199.556i
43.6		−	4.41884i	12.1965			−3.52613			8.95876				−	53.8945i			18.5203i		−	55.1200i	67.7552				−	39.5873i
43.7		−	4.21793i	2.13750			−1.79093			−12.8170				−	9.01583i		−	18.5203i		−	59.9329i	−76.4311					54.0612i
43.8		−	3.63309i	−14.5092			2.80065			40.9010					52.7134i		−	18.5203i		−	68.3045i	129.518				−	148.597i
43.9		−	2.63129i	15.8544			9.07633			−7.06095				−	41.7174i		−	18.5203i		−	65.9830i	170.361					18.5794i
43.10		−	2.45946i	−5.74524			9.95104			−18.9187					14.1302i			18.5203i		−	63.8256i	−47.9922					46.5298i
43.11		−	1.16652i	−10.9041			14.6392			1.51619					12.7199i			18.5203i		−	35.7413i	37.8993				−	1.76867i
43.12		−	0.289338i	5.30109			15.9163			31.9208				−	1.53381i		−	18.5203i		−	9.23460i	−52.8985				−	9.23590i
43.13			0.289338i	5.30109			15.9163			31.9208					1.53381i			18.5203i			9.23460i	−52.8985					9.23590i
43.14			1.16652i	−10.9041			14.6392			1.51619				−	12.7199i		−	18.5203i			35.7413i	37.8993					1.76867i
43.15			2.45946i	−5.74524			9.95104			−18.9187				−	14.1302i		−	18.5203i			63.8256i	−47.9922				−	46.5298i
43.16			2.63129i	15.8544			9.07633			−7.06095					41.7174i			18.5203i			65.9830i	170.361				−	18.5794i
43.17			3.63309i	−14.5092			2.80065			40.9010				−	52.7134i			18.5203i			68.3045i	129.518					148.597i
43.18			4.21793i	2.13750			−1.79093			−12.8170					9.01583i			18.5203i			59.9329i	−76.4311				−	54.0612i
43.19			4.41884i	12.1965			−3.52613			8.95876					53.8945i		−	18.5203i			55.1200i	67.7552					39.5873i
43.20			4.80284i	−16.4118			−7.06726			−41.5497				−	78.8230i			18.5203i			42.9025i	188.346				−	199.556i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	77.5.c.a	✓	24
11.b	odd	2	1	inner	77.5.c.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
77.5.c.a	✓	24	1.a	even	1	1	trivial
77.5.c.a	✓	24	11.b	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(77, [\chi])\).