Newform orbit 154.4.c.a

• Label: 154.4.c.a
• Level: $154$
• Weight: $4$
• Character orbit: 154.c
• Analytic conductor: $9.086$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$154 = 2 \cdot 7 \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	154.c (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$9.08629414088$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

$\operatorname{Tr}(f)(q) =$ 24 * q - 96 * q^4 - 152 * q^9 + 36 * q^11 - 32 * q^14 - 248 * q^15 + 384 * q^16 + 184 * q^22 - 392 * q^23 - 56 * q^25 + 608 * q^36 + 720 * q^37 + 576 * q^42 - 144 * q^44 - 1472 * q^49 - 2744 * q^53 + 128 * q^56 + 1680 * q^58 + 992 * q^60 - 1536 * q^64 + 2048 * q^67 + 672 * q^70 - 760 * q^71 + 2532 * q^77 - 1040 * q^78 - 3984 * q^81 + 736 * q^86 - 736 * q^88 - 824 * q^91 + 1568 * q^92 + 4560 * q^93 + 4220 * q^99

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
153.1		−	2.00000i		−	8.81399i	−4.00000				−	3.81914i	−17.6280			−6.10201	+	17.4862i			8.00000i	−50.6865			−7.63828
153.2		−	2.00000i		−	7.37278i	−4.00000				−	19.4906i	−14.7456			−1.31020	−	18.4739i			8.00000i	−27.3578			−38.9812
153.3		−	2.00000i		−	6.22079i	−4.00000					7.04818i	−12.4416			−15.3222	−	10.4034i			8.00000i	−11.6982			14.0964
153.4		−	2.00000i		−	3.65107i	−4.00000					9.62869i	−7.30215			−1.84269	+	18.4284i			8.00000i	13.6697			19.2574
153.5		−	2.00000i		−	3.50992i	−4.00000					13.7268i	−7.01983			18.5195	−	0.170481i			8.00000i	14.6805			27.4536
153.6		−	2.00000i		−	1.89937i	−4.00000				−	6.22238i	−3.79874			14.9971	−	10.8668i			8.00000i	23.3924			−12.4448
153.7		−	2.00000i			1.89937i	−4.00000					6.22238i	3.79874			−14.9971	−	10.8668i			8.00000i	23.3924			12.4448
153.8		−	2.00000i			3.50992i	−4.00000				−	13.7268i	7.01983			−18.5195	−	0.170481i			8.00000i	14.6805			−27.4536
153.9		−	2.00000i			3.65107i	−4.00000				−	9.62869i	7.30215			1.84269	+	18.4284i			8.00000i	13.6697			−19.2574
153.10		−	2.00000i			6.22079i	−4.00000				−	7.04818i	12.4416			15.3222	−	10.4034i			8.00000i	−11.6982			−14.0964
153.11		−	2.00000i			7.37278i	−4.00000					19.4906i	14.7456			1.31020	−	18.4739i			8.00000i	−27.3578			38.9812
153.12		−	2.00000i			8.81399i	−4.00000					3.81914i	17.6280			6.10201	+	17.4862i			8.00000i	−50.6865			7.63828
153.13			2.00000i		−	8.81399i	−4.00000				−	3.81914i	17.6280			6.10201	−	17.4862i		−	8.00000i	−50.6865			7.63828
153.14			2.00000i		−	7.37278i	−4.00000				−	19.4906i	14.7456			1.31020	+	18.4739i		−	8.00000i	−27.3578			38.9812
153.15			2.00000i		−	6.22079i	−4.00000					7.04818i	12.4416			15.3222	+	10.4034i		−	8.00000i	−11.6982			−14.0964
153.16			2.00000i		−	3.65107i	−4.00000					9.62869i	7.30215			1.84269	−	18.4284i		−	8.00000i	13.6697			−19.2574
153.17			2.00000i		−	3.50992i	−4.00000					13.7268i	7.01983			−18.5195	+	0.170481i		−	8.00000i	14.6805			−27.4536
153.18			2.00000i		−	1.89937i	−4.00000				−	6.22238i	3.79874			−14.9971	+	10.8668i		−	8.00000i	23.3924			12.4448
153.19			2.00000i			1.89937i	−4.00000					6.22238i	−3.79874			14.9971	+	10.8668i		−	8.00000i	23.3924			−12.4448
153.20			2.00000i			3.50992i	−4.00000				−	13.7268i	−7.01983			18.5195	+	0.170481i		−	8.00000i	14.6805			27.4536

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	154.4.c.a	✓	24
7.b	odd	2	1	inner	154.4.c.a	✓	24
11.b	odd	2	1	inner	154.4.c.a	✓	24
77.b	even	2	1	inner	154.4.c.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
154.4.c.a	✓	24	1.a	even	1	1	trivial
154.4.c.a	✓	24	7.b	odd	2	1	inner
154.4.c.a	✓	24	11.b	odd	2	1	inner
154.4.c.a	✓	24	77.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace $S_{4}^{\mathrm{new}}(154, [\chi])$.