Newform orbit 175.2.o.d

• Label: 175.2.o.d
• Level: $175$
• Weight: $2$
• Character orbit: 175.o
• Analytic conductor: $1.397$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.o (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.39738203537\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 8 q^{11} - 4 q^{16} - 28 q^{21} + 12 q^{26} - 36 q^{31} - 8 q^{36} - 8 q^{46} + 36 q^{51} - 60 q^{56} + 84 q^{61} + 168 q^{66} - 136 q^{71} - 20 q^{81} - 80 q^{86} + 20 q^{91} - 60 q^{96}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
68.1	−0.647225	−	2.41547i	−2.17663	−	0.583228i	−3.68357	+	2.12671i		0				5.63509i	−0.373780	+	2.61922i	3.98461	+	3.98461i	1.79951	+	1.03895i		0
68.2	−0.485585	−	1.81223i	−0.463674	−	0.124241i	−1.31633	+	0.759985i		0				0.900613i	−1.92108	−	1.81919i	−0.636830	−	0.636830i	−2.39852	−	1.38479i		0
68.3	−0.286649	−	1.06979i	2.67889	+	0.717805i	0.669773	−	0.386694i		0			−	3.07160i	−2.58258	−	0.574697i	−2.17195	−	2.17195i	4.06311	+	2.34584i		0
68.4	0.286649	+	1.06979i	−2.67889	−	0.717805i	0.669773	−	0.386694i		0			−	3.07160i	2.58258	+	0.574697i	2.17195	+	2.17195i	4.06311	+	2.34584i		0
68.5	0.485585	+	1.81223i	0.463674	+	0.124241i	−1.31633	+	0.759985i		0				0.900613i	1.92108	+	1.81919i	0.636830	+	0.636830i	−2.39852	−	1.38479i		0
68.6	0.647225	+	2.41547i	2.17663	+	0.583228i	−3.68357	+	2.12671i		0				5.63509i	0.373780	−	2.61922i	−3.98461	−	3.98461i	1.79951	+	1.03895i		0
82.1	−2.41547	+	0.647225i	0.583228	−	2.17663i	3.68357	−	2.12671i		0				5.63509i	2.61922	+	0.373780i	−3.98461	+	3.98461i	−1.79951	−	1.03895i		0
82.2	−1.81223	+	0.485585i	0.124241	−	0.463674i	1.31633	−	0.759985i		0				0.900613i	−1.81919	+	1.92108i	0.636830	−	0.636830i	2.39852	+	1.38479i		0
82.3	−1.06979	+	0.286649i	−0.717805	+	2.67889i	−0.669773	+	0.386694i		0			−	3.07160i	−0.574697	+	2.58258i	2.17195	−	2.17195i	−4.06311	−	2.34584i		0
82.4	1.06979	−	0.286649i	0.717805	−	2.67889i	−0.669773	+	0.386694i		0			−	3.07160i	0.574697	−	2.58258i	−2.17195	+	2.17195i	−4.06311	−	2.34584i		0
82.5	1.81223	−	0.485585i	−0.124241	+	0.463674i	1.31633	−	0.759985i		0				0.900613i	1.81919	−	1.92108i	−0.636830	+	0.636830i	2.39852	+	1.38479i		0
82.6	2.41547	−	0.647225i	−0.583228	+	2.17663i	3.68357	−	2.12671i		0				5.63509i	−2.61922	−	0.373780i	3.98461	−	3.98461i	−1.79951	−	1.03895i		0
143.1	−2.41547	−	0.647225i	0.583228	+	2.17663i	3.68357	+	2.12671i		0			−	5.63509i	2.61922	−	0.373780i	−3.98461	−	3.98461i	−1.79951	+	1.03895i		0
143.2	−1.81223	−	0.485585i	0.124241	+	0.463674i	1.31633	+	0.759985i		0			−	0.900613i	−1.81919	−	1.92108i	0.636830	+	0.636830i	2.39852	−	1.38479i		0
143.3	−1.06979	−	0.286649i	−0.717805	−	2.67889i	−0.669773	−	0.386694i		0				3.07160i	−0.574697	−	2.58258i	2.17195	+	2.17195i	−4.06311	+	2.34584i		0
143.4	1.06979	+	0.286649i	0.717805	+	2.67889i	−0.669773	−	0.386694i		0				3.07160i	0.574697	+	2.58258i	−2.17195	−	2.17195i	−4.06311	+	2.34584i		0
143.5	1.81223	+	0.485585i	−0.124241	−	0.463674i	1.31633	+	0.759985i		0			−	0.900613i	1.81919	+	1.92108i	−0.636830	−	0.636830i	2.39852	−	1.38479i		0
143.6	2.41547	+	0.647225i	−0.583228	−	2.17663i	3.68357	+	2.12671i		0			−	5.63509i	−2.61922	+	0.373780i	3.98461	+	3.98461i	−1.79951	+	1.03895i		0
157.1	−0.647225	+	2.41547i	−2.17663	+	0.583228i	−3.68357	−	2.12671i		0			−	5.63509i	−0.373780	−	2.61922i	3.98461	−	3.98461i	1.79951	−	1.03895i		0
157.2	−0.485585	+	1.81223i	−0.463674	+	0.124241i	−1.31633	−	0.759985i		0			−	0.900613i	−1.92108	+	1.81919i	−0.636830	+	0.636830i	−2.39852	+	1.38479i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
5.c	odd	4	2	inner
7.d	odd	6	1	inner
35.i	odd	6	1	inner
35.k	even	12	2	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	175.2.o.d	✓	24
5.b	even	2	1	inner	175.2.o.d	✓	24
5.c	odd	4	2	inner	175.2.o.d	✓	24
7.d	odd	6	1	inner	175.2.o.d	✓	24
35.i	odd	6	1	inner	175.2.o.d	✓	24
35.k	even	12	2	inner	175.2.o.d	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
175.2.o.d	✓	24	1.a	even	1	1	trivial
175.2.o.d	✓	24	5.b	even	2	1	inner
175.2.o.d	✓	24	5.c	odd	4	2	inner
175.2.o.d	✓	24	7.d	odd	6	1	inner
175.2.o.d	✓	24	35.i	odd	6	1	inner
175.2.o.d	✓	24	35.k	even	12	2	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} - 53T_{2}^{20} + 2247T_{2}^{16} - 28328T_{2}^{12} + 277207T_{2}^{8} - 409698T_{2}^{4} + 531441 \) acting on \(S_{2}^{\mathrm{new}}(175, [\chi])\).