Newform orbit 1127.2.c.b

• Label: 1127.2.c.b
• Level: $1127$
• Weight: $2$
• Character orbit: 1127.c
• Analytic conductor: $8.999$
• Analytic rank: $0$
• Dimension: $24$
• CM discriminant: -23
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1127 = 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1127.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.99914030780\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 48 q^{4} - 72 q^{9} + 96 q^{16} - 120 q^{25} - 144 q^{36} + 192 q^{64} + 216 q^{81}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1126.1	−2.82038				−	1.72965i	5.95452				0				4.87826i		0		−11.1532			0.00831203				0
1126.2	−2.82038					1.72965i	5.95452				0			−	4.87826i		0		−11.1532			0.00831203				0
1126.3	−2.54915					3.34678i	4.49815				0			−	8.53143i		0		−6.36814			−8.20095				0
1126.4	−2.54915				−	3.34678i	4.49815				0				8.53143i		0		−6.36814			−8.20095				0
1126.5	−2.33589					2.45145i	3.45638				0			−	5.72631i		0		−3.40193			−3.00960				0
1126.6	−2.33589				−	2.45145i	3.45638				0				5.72631i		0		−3.40193			−3.00960				0
1126.7	−1.59487				−	0.00277196i	0.543624				0				0.00442092i		0		2.32274			2.99999				0
1126.8	−1.59487					0.00277196i	0.543624				0			−	0.00442092i		0		2.32274			2.99999				0
1126.9	−1.22550				−	2.99861i	−0.498145				0				3.67481i		0		3.06148			−5.99168				0
1126.10	−1.22550					2.99861i	−0.498145				0			−	3.67481i		0		3.06148			−5.99168				0
1126.11	−0.213257					3.34535i	−1.95452				0			−	0.713419i		0		0.843330			−8.19134				0
1126.12	−0.213257				−	3.34535i	−1.95452				0				0.713419i		0		0.843330			−8.19134				0
1126.13	0.213257				−	0.899253i	−1.95452				0			−	0.191772i		0		−0.843330			2.19134				0
1126.14	0.213257					0.899253i	−1.95452				0				0.191772i		0		−0.843330			2.19134				0
1126.15	1.22550				−	1.73445i	−0.498145				0			−	2.12557i		0		−3.06148			−0.00831971				0
1126.16	1.22550					1.73445i	−0.498145				0				2.12557i		0		−3.06148			−0.00831971				0
1126.17	1.59487					3.46410i	0.543624				0				5.52480i		0		−2.32274			−8.99999				0
1126.18	1.59487				−	3.46410i	0.543624				0			−	5.52480i		0		−2.32274			−8.99999				0
1126.19	2.33589					2.44753i	3.45638				0				5.71716i		0		3.40193			−2.99040				0
1126.20	2.33589				−	2.44753i	3.45638				0			−	5.71716i		0		3.40193			−2.99040				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.b	odd	2	1	CM by \(\Q(\sqrt{-23}) \)
7.b	odd	2	1	inner
161.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1127.2.c.b	✓	24
7.b	odd	2	1	inner	1127.2.c.b	✓	24
23.b	odd	2	1	CM	1127.2.c.b	✓	24
161.c	even	2	1	inner	1127.2.c.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1127.2.c.b	✓	24	1.a	even	1	1	trivial
1127.2.c.b	✓	24	7.b	odd	2	1	inner
1127.2.c.b	✓	24	23.b	odd	2	1	CM
1127.2.c.b	✓	24	161.c	even	2	1	inner