Newform orbit 405.5.c.b

• Label: 405.5.c.b
• Level: $405$
• Weight: $5$
• Character orbit: 405.c
• Analytic conductor: $41.865$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	405.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(41.8648350490\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	no (minimal twist has level 45)
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.

\(\operatorname{Tr}(f)(q) = \) 32 * q - 256 * q^4 + 52 * q^7 - 20 * q^13 + 2048 * q^16 + 508 * q^19 - 1344 * q^22 - 4000 * q^25 - 1664 * q^28 + 2944 * q^31 + 1188 * q^34 + 2068 * q^37 - 3300 * q^40 - 1136 * q^43 + 5724 * q^46 + 3348 * q^49 - 3068 * q^52 + 16380 * q^58 + 8956 * q^61 - 37216 * q^64 - 25676 * q^67 - 4800 * q^70 + 29236 * q^73 - 12380 * q^76 + 7024 * q^79 + 34692 * q^82 + 8700 * q^85 + 32256 * q^88 - 48904 * q^91 - 10236 * q^94 - 46532 * q^97

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
161.1		−	7.94106i		0		−47.0604					11.1803i		0		−20.2472					246.652i		0		88.7837
161.2		−	7.29275i		0		−37.1842				−	11.1803i		0		51.7649					154.491i		0		−81.5354
161.3		−	6.85584i		0		−31.0026				−	11.1803i		0		−25.1046					102.855i		0		−76.6506
161.4		−	6.65381i		0		−28.2732					11.1803i		0		86.7729					81.6633i		0		74.3918
161.5		−	6.03767i		0		−20.4535				−	11.1803i		0		16.2628					26.8889i		0		−67.5033
161.6		−	5.90236i		0		−18.8378					11.1803i		0		−72.3212					16.7497i		0		65.9903
161.7		−	5.52783i		0		−14.5570					11.1803i		0		1.64066				−	7.97692i		0		61.8031
161.8		−	3.89522i		0		0.827263				−	11.1803i		0		−31.0349				−	65.5459i		0		−43.5499
161.9		−	3.73920i		0		2.01838				−	11.1803i		0		39.4150				−	67.3743i		0		−41.8055
161.10		−	3.73710i		0		2.03405					11.1803i		0		−16.0585				−	67.3951i		0		41.7821
161.11		−	3.58617i		0		3.13937				−	11.1803i		0		−91.8108				−	68.6371i		0		−40.0946
161.12		−	2.99787i		0		7.01276					11.1803i		0		3.27438				−	68.9893i		0		33.5172
161.13		−	2.48322i		0		9.83359				−	11.1803i		0		31.5696				−	64.1506i		0		−27.7633
161.14		−	1.23097i		0		14.4847					11.1803i		0		42.2629				−	37.5258i		0		13.7627
161.15		−	1.04455i		0		14.9089				−	11.1803i		0		72.9965				−	32.2860i		0		−11.6784
161.16		−	0.943633i		0		15.1096					11.1803i		0		−63.3825				−	29.3560i		0		10.5501
161.17			0.943633i		0		15.1096				−	11.1803i		0		−63.3825					29.3560i		0		10.5501
161.18			1.04455i		0		14.9089					11.1803i		0		72.9965					32.2860i		0		−11.6784
161.19			1.23097i		0		14.4847				−	11.1803i		0		42.2629					37.5258i		0		13.7627
161.20			2.48322i		0		9.83359					11.1803i		0		31.5696					64.1506i		0		−27.7633

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	405.5.c.b		32
3.b	odd	2	1	inner	405.5.c.b		32
9.c	even	3	1		45.5.i.a	✓	32
9.c	even	3	1		135.5.i.a		32
9.d	odd	6	1		45.5.i.a	✓	32
9.d	odd	6	1		135.5.i.a		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
45.5.i.a	✓	32	9.c	even	3	1
45.5.i.a	✓	32	9.d	odd	6	1
135.5.i.a		32	9.c	even	3	1
135.5.i.a		32	9.d	odd	6	1
405.5.c.b		32	1.a	even	1	1	trivial
405.5.c.b		32	3.b	odd	2	1	inner