Newform orbit 1155.2.i.d

• Label: 1155.2.i.d
• Level: $1155$
• Weight: $2$
• Character orbit: 1155.i
• Analytic conductor: $9.223$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.i (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.22272143346\)
Analytic rank:	\(0\)
Dimension:	\(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
76.1		−	1.26491i		−	1.00000i	0.399993				−	1.00000i	−1.26491			0.0556365	−	2.64517i		−	3.03578i	−1.00000			−1.26491
76.2			1.26491i			1.00000i	0.399993					1.00000i	−1.26491			0.0556365	+	2.64517i			3.03578i	−1.00000			−1.26491
76.3		−	0.370647i		−	1.00000i	1.86262				−	1.00000i	−0.370647			−2.39596	+	1.12222i		−	1.43167i	−1.00000			−0.370647
76.4			0.370647i			1.00000i	1.86262					1.00000i	−0.370647			−2.39596	−	1.12222i			1.43167i	−1.00000			−0.370647
76.5		−	2.40558i		−	1.00000i	−3.78682				−	1.00000i	−2.40558			1.69010	−	2.03557i			4.29833i	−1.00000			−2.40558
76.6			2.40558i			1.00000i	−3.78682					1.00000i	−2.40558			1.69010	+	2.03557i		−	4.29833i	−1.00000			−2.40558
76.7		−	2.76869i		−	1.00000i	−5.66565				−	1.00000i	−2.76869			−2.02228	−	1.70599i			10.1491i	−1.00000			−2.76869
76.8			2.76869i			1.00000i	−5.66565					1.00000i	−2.76869			−2.02228	+	1.70599i		−	10.1491i	−1.00000			−2.76869
76.9		−	0.859876i			1.00000i	1.26061					1.00000i	0.859876			−2.42783	−	1.05149i		−	2.80372i	−1.00000			0.859876
76.10			0.859876i		−	1.00000i	1.26061				−	1.00000i	0.859876			−2.42783	+	1.05149i			2.80372i	−1.00000			0.859876
76.11		−	1.29033i		−	1.00000i	0.335051				−	1.00000i	−1.29033			2.23077	+	1.42256i		−	3.01298i	−1.00000			−1.29033
76.12			1.29033i			1.00000i	0.335051					1.00000i	−1.29033			2.23077	−	1.42256i			3.01298i	−1.00000			−1.29033
76.13		−	1.54704i		−	1.00000i	−0.393347				−	1.00000i	−1.54704			−2.51711	−	0.814965i		−	2.48556i	−1.00000			−1.54704
76.14			1.54704i			1.00000i	−0.393347					1.00000i	−1.54704			−2.51711	+	0.814965i			2.48556i	−1.00000			−1.54704
76.15		−	2.23885i		−	1.00000i	−3.01246				−	1.00000i	−2.23885			−0.322004	+	2.62608i			2.26674i	−1.00000			−2.23885
76.16			2.23885i			1.00000i	−3.01246					1.00000i	−2.23885			−0.322004	−	2.62608i		−	2.26674i	−1.00000			−2.23885
76.17		−	2.23885i			1.00000i	−3.01246					1.00000i	2.23885			0.322004	+	2.62608i			2.26674i	−1.00000			2.23885
76.18			2.23885i		−	1.00000i	−3.01246				−	1.00000i	2.23885			0.322004	−	2.62608i		−	2.26674i	−1.00000			2.23885
76.19		−	1.54704i			1.00000i	−0.393347					1.00000i	1.54704			2.51711	−	0.814965i		−	2.48556i	−1.00000			1.54704
76.20			1.54704i		−	1.00000i	−0.393347				−	1.00000i	1.54704			2.51711	+	0.814965i			2.48556i	−1.00000			1.54704

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	1155.2.i.d	✓	32
7.b	odd	2	1	inner	1155.2.i.d	✓	32
11.b	odd	2	1	inner	1155.2.i.d	✓	32
77.b	even	2	1	inner	1155.2.i.d	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1155.2.i.d	✓	32	1.a	even	1	1	trivial
1155.2.i.d	✓	32	7.b	odd	2	1	inner
1155.2.i.d	✓	32	11.b	odd	2	1	inner
1155.2.i.d	✓	32	77.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{16} + 25T_{2}^{14} + 248T_{2}^{12} + 1256T_{2}^{10} + 3495T_{2}^{8} + 5383T_{2}^{6} + 4344T_{2}^{4} + 1552T_{2}^{2} + 144 \) acting on \(S_{2}^{\mathrm{new}}(1155, [\chi])\).