Newform orbit 1150.3.d.e

• Label: 1150.3.d.e
• Level: $1150$
• Weight: $3$
• Character orbit: 1150.d
• Analytic conductor: $31.335$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(31.3352304014\)
Analytic rank:	\(0\)
Dimension:	\(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 48 q^{4} + 8 q^{6} + 96 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
551.1	−1.41421			−5.56886			2.00000				0		7.87556					10.0249i	−2.82843			22.0122				0
551.2	−1.41421			−3.00625			2.00000				0		4.25149					7.53698i	−2.82843			0.0375672				0
551.3	−1.41421			2.29017			2.00000				0		−3.23879				−	9.92340i	−2.82843			−3.75511				0
551.4	−1.41421			5.45221			2.00000				0		−7.71059				−	0.770899i	−2.82843			20.7266				0
551.5	−1.41421			0.894518			2.00000				0		−1.26504					4.24317i	−2.82843			−8.19984				0
551.6	−1.41421			−1.47600			2.00000				0		2.08738					0.788814i	−2.82843			−6.82142				0
551.7	−1.41421			−1.47600			2.00000				0		2.08738				−	0.788814i	−2.82843			−6.82142				0
551.8	−1.41421			0.894518			2.00000				0		−1.26504				−	4.24317i	−2.82843			−8.19984				0
551.9	−1.41421			5.45221			2.00000				0		−7.71059					0.770899i	−2.82843			20.7266				0
551.10	−1.41421			2.29017			2.00000				0		−3.23879					9.92340i	−2.82843			−3.75511				0
551.11	−1.41421			−3.00625			2.00000				0		4.25149				−	7.53698i	−2.82843			0.0375672				0
551.12	−1.41421			−5.56886			2.00000				0		7.87556				−	10.0249i	−2.82843			22.0122				0
551.13	1.41421			5.56886			2.00000				0		7.87556					10.0249i	2.82843			22.0122				0
551.14	1.41421			3.00625			2.00000				0		4.25149					7.53698i	2.82843			0.0375672				0
551.15	1.41421			−2.29017			2.00000				0		−3.23879				−	9.92340i	2.82843			−3.75511				0
551.16	1.41421			−5.45221			2.00000				0		−7.71059				−	0.770899i	2.82843			20.7266				0
551.17	1.41421			−0.894518			2.00000				0		−1.26504					4.24317i	2.82843			−8.19984				0
551.18	1.41421			1.47600			2.00000				0		2.08738					0.788814i	2.82843			−6.82142				0
551.19	1.41421			1.47600			2.00000				0		2.08738				−	0.788814i	2.82843			−6.82142				0
551.20	1.41421			−0.894518			2.00000				0		−1.26504				−	4.24317i	2.82843			−8.19984				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.d.e		24
5.b	even	2	1	inner	1150.3.d.e		24
5.c	odd	4	2		230.3.c.a	✓	24
23.b	odd	2	1	inner	1150.3.d.e		24
115.c	odd	2	1	inner	1150.3.d.e		24
115.e	even	4	2		230.3.c.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
230.3.c.a	✓	24	5.c	odd	4	2
230.3.c.a	✓	24	115.e	even	4	2
1150.3.d.e		24	1.a	even	1	1	trivial
1150.3.d.e		24	5.b	even	2	1	inner
1150.3.d.e		24	23.b	odd	2	1	inner
1150.3.d.e		24	115.c	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} - 78T_{3}^{10} + 2062T_{3}^{8} - 21648T_{3}^{6} + 94697T_{3}^{4} - 158138T_{3}^{2} + 76176 \) acting on \(S_{3}^{\mathrm{new}}(1150, [\chi])\).