Newform orbit 608.2.bi.a

• Label: 608.2.bi.a
• Level: $608$
• Weight: $2$
• Character orbit: 608.bi
• Analytic conductor: $4.855$
• Analytic rank: $0$
• Dimension: $120$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.bi (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.85490444289\)
Analytic rank:	\(0\)
Dimension:	\(120\)
Relative dimension:	\(20\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 120 q - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
127.1		0		−2.88658	−	1.05063i		0		0.707424	+	4.01200i		0		1.03166	+	0.595627i		0		4.93037	+	4.13707i		0
127.2		0		−2.79073	−	1.01574i		0		−0.0237985	−	0.134968i		0		0.566924	+	0.327314i		0		4.45829	+	3.74095i		0
127.3		0		−2.72583	−	0.992120i		0		−0.438120	−	2.48470i		0		−4.02479	−	2.32371i		0		4.14771	+	3.48034i		0
127.4		0		−1.96670	−	0.715821i		0		−0.702518	−	3.98418i		0		1.37687	+	0.794938i		0		1.05739	+	0.887252i		0
127.5		0		−1.81738	−	0.661474i		0		0.368367	+	2.08911i		0		−2.28549	−	1.31953i		0		0.567206	+	0.475942i		0
127.6		0		−1.62452	−	0.591278i		0		−0.199718	−	1.13266i		0		4.42484	+	2.55468i		0		−0.00866713	−	0.00727259i		0
127.7		0		−1.40442	−	0.511167i		0		−0.167737	−	0.951284i		0		−2.41083	−	1.39189i		0		−0.587028	−	0.492575i		0
127.8		0		−0.701136	−	0.255193i		0		−0.205536	−	1.16565i		0		2.59188	+	1.49642i		0		−1.87167	−	1.57051i		0
127.9		0		−0.330616	−	0.120334i		0		0.0498539	+	0.282736i		0		−0.0995693	−	0.0574864i		0		−2.20331	−	1.84879i		0
127.10		0		−0.0209646	−	0.00763049i		0		0.611783	+	3.46959i		0		2.05401	+	1.18588i		0		−2.29775	−	1.92804i		0
127.11		0		0.0209646	+	0.00763049i		0		0.611783	+	3.46959i		0		−2.05401	−	1.18588i		0		−2.29775	−	1.92804i		0
127.12		0		0.330616	+	0.120334i		0		0.0498539	+	0.282736i		0		0.0995693	+	0.0574864i		0		−2.20331	−	1.84879i		0
127.13		0		0.701136	+	0.255193i		0		−0.205536	−	1.16565i		0		−2.59188	−	1.49642i		0		−1.87167	−	1.57051i		0
127.14		0		1.40442	+	0.511167i		0		−0.167737	−	0.951284i		0		2.41083	+	1.39189i		0		−0.587028	−	0.492575i		0
127.15		0		1.62452	+	0.591278i		0		−0.199718	−	1.13266i		0		−4.42484	−	2.55468i		0		−0.00866713	−	0.00727259i		0
127.16		0		1.81738	+	0.661474i		0		0.368367	+	2.08911i		0		2.28549	+	1.31953i		0		0.567206	+	0.475942i		0
127.17		0		1.96670	+	0.715821i		0		−0.702518	−	3.98418i		0		−1.37687	−	0.794938i		0		1.05739	+	0.887252i		0
127.18		0		2.72583	+	0.992120i		0		−0.438120	−	2.48470i		0		4.02479	+	2.32371i		0		4.14771	+	3.48034i		0
127.19		0		2.79073	+	1.01574i		0		−0.0237985	−	0.134968i		0		−0.566924	−	0.327314i		0		4.45829	+	3.74095i		0
127.20		0		2.88658	+	1.05063i		0		0.707424	+	4.01200i		0		−1.03166	−	0.595627i		0		4.93037	+	4.13707i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
19.f	odd	18	1	inner
76.k	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	608.2.bi.a	✓	120
4.b	odd	2	1	inner	608.2.bi.a	✓	120
19.f	odd	18	1	inner	608.2.bi.a	✓	120
76.k	even	18	1	inner	608.2.bi.a	✓	120

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
608.2.bi.a	✓	120	1.a	even	1	1	trivial
608.2.bi.a	✓	120	4.b	odd	2	1	inner
608.2.bi.a	✓	120	19.f	odd	18	1	inner
608.2.bi.a	✓	120	76.k	even	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(608, [\chi])\).