Newform orbit 1150.3.c.c

• Label: 1150.3.c.c
• Level: $1150$
• Weight: $3$
• Character orbit: 1150.c
• Analytic conductor: $31.335$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(31.3352304014\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	no (minimal twist has level 230)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1149.1		−	1.41421i			1.43837i	−2.00000				0		2.03417			−10.1866					2.82843i	6.93108				0
1149.2			1.41421i		−	1.43837i	−2.00000				0		2.03417			−10.1866				−	2.82843i	6.93108				0
1149.3		−	1.41421i			5.41949i	−2.00000				0		7.66432			8.24199					2.82843i	−20.3709				0
1149.4			1.41421i		−	5.41949i	−2.00000				0		7.66432			8.24199				−	2.82843i	−20.3709				0
1149.5		−	1.41421i		−	4.76369i	−2.00000				0		−6.73687			−7.05858					2.82843i	−13.6927				0
1149.6			1.41421i			4.76369i	−2.00000				0		−6.73687			−7.05858				−	2.82843i	−13.6927				0
1149.7		−	1.41421i			0.278523i	−2.00000				0		0.393890			8.51262					2.82843i	8.92243				0
1149.8			1.41421i		−	0.278523i	−2.00000				0		0.393890			8.51262				−	2.82843i	8.92243				0
1149.9		−	1.41421i		−	3.79379i	−2.00000				0		−5.36524			−7.10180					2.82843i	−5.39287				0
1149.10			1.41421i			3.79379i	−2.00000				0		−5.36524			−7.10180				−	2.82843i	−5.39287				0
1149.11		−	1.41421i		−	2.34854i	−2.00000				0		−3.32134			7.61815					2.82843i	3.48436				0
1149.12			1.41421i			2.34854i	−2.00000				0		−3.32134			7.61815				−	2.82843i	3.48436				0
1149.13		−	1.41421i			4.30716i	−2.00000				0		6.09125			−1.47532					2.82843i	−9.55167				0
1149.14			1.41421i		−	4.30716i	−2.00000				0		6.09125			−1.47532				−	2.82843i	−9.55167				0
1149.15		−	1.41421i		−	3.36596i	−2.00000				0		−4.76019			1.16919					2.82843i	−2.32968				0
1149.16			1.41421i			3.36596i	−2.00000				0		−4.76019			1.16919				−	2.82843i	−2.32968				0
1149.17		−	1.41421i		−	3.36596i	−2.00000				0		−4.76019			−1.16919					2.82843i	−2.32968				0
1149.18			1.41421i			3.36596i	−2.00000				0		−4.76019			−1.16919				−	2.82843i	−2.32968				0
1149.19		−	1.41421i			4.30716i	−2.00000				0		6.09125			1.47532					2.82843i	−9.55167				0
1149.20			1.41421i		−	4.30716i	−2.00000				0		6.09125			1.47532				−	2.82843i	−9.55167				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
23.b	odd	2	1	inner
115.c	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1150.3.c.c		32
5.b	even	2	1	inner	1150.3.c.c		32
5.c	odd	4	1		230.3.d.a	✓	16
5.c	odd	4	1		1150.3.d.b		16
15.e	even	4	1		2070.3.c.a		16
20.e	even	4	1		1840.3.k.d		16
23.b	odd	2	1	inner	1150.3.c.c		32
115.c	odd	2	1	inner	1150.3.c.c		32
115.e	even	4	1		230.3.d.a	✓	16
115.e	even	4	1		1150.3.d.b		16
345.l	odd	4	1		2070.3.c.a		16
460.k	odd	4	1		1840.3.k.d		16

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
230.3.d.a	✓	16	5.c	odd	4	1
230.3.d.a	✓	16	115.e	even	4	1
1150.3.c.c		32	1.a	even	1	1	trivial
1150.3.c.c		32	5.b	even	2	1	inner
1150.3.c.c		32	23.b	odd	2	1	inner
1150.3.c.c		32	115.c	odd	2	1	inner
1150.3.d.b		16	5.c	odd	4	1
1150.3.d.b		16	115.e	even	4	1
1840.3.k.d		16	20.e	even	4	1
1840.3.k.d		16	460.k	odd	4	1
2070.3.c.a		16	15.e	even	4	1
2070.3.c.a		16	345.l	odd	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^16 + 104*T3^14 + 4362*T3^12 + 94700*T3^10 + 1132361*T3^8 + 7286420*T3^6 + 22518132*T3^4 + 24712224*T3^2 + 1784896