Newform orbit 100.7.d.c

• Label: 100.7.d.c
• Level: $100$
• Weight: $7$
• Character orbit: 100.d
• Analytic conductor: $23.005$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(23.0054083620\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 42 q^{4} + 186 q^{6} + 6752 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
99.1	−7.79172	−	1.81357i	5.61619			57.4219	+	28.2617i		0		−43.7598	−	10.1854i	168.612			−396.161	−	324.346i	−697.458				0
99.2	−7.79172	+	1.81357i	5.61619			57.4219	−	28.2617i		0		−43.7598	+	10.1854i	168.612			−396.161	+	324.346i	−697.458				0
99.3	−6.70332	−	4.36640i	42.9484			25.8690	+	58.5388i		0		−287.897	−	187.530i	−563.855			82.1957	−	505.359i	1115.56				0
99.4	−6.70332	+	4.36640i	42.9484			25.8690	−	58.5388i		0		−287.897	+	187.530i	−563.855			82.1957	+	505.359i	1115.56				0
99.5	−6.27431	−	4.96317i	−26.0537			14.7338	+	62.2809i		0		163.469	+	129.309i	195.627			216.667	−	463.896i	−50.2058				0
99.6	−6.27431	+	4.96317i	−26.0537			14.7338	−	62.2809i		0		163.469	−	129.309i	195.627			216.667	+	463.896i	−50.2058				0
99.7	−5.75952	−	5.55229i	−49.8952			2.34412	+	63.9571i		0		287.372	+	277.032i	−331.710			341.607	−	381.377i	1760.53				0
99.8	−5.75952	+	5.55229i	−49.8952			2.34412	−	63.9571i		0		287.372	−	277.032i	−331.710			341.607	+	381.377i	1760.53				0
99.9	−2.90251	−	7.45489i	22.0610			−47.1509	+	43.2758i		0		−64.0322	−	164.462i	−85.8808			459.472	+	225.897i	−242.313				0
99.10	−2.90251	+	7.45489i	22.0610			−47.1509	−	43.2758i		0		−64.0322	+	164.462i	−85.8808			459.472	−	225.897i	−242.313				0
99.11	−0.375512	−	7.99118i	23.0410			−63.7180	+	6.00157i		0		−8.65216	−	184.125i	631.848			71.8865	+	506.928i	−198.114				0
99.12	−0.375512	+	7.99118i	23.0410			−63.7180	−	6.00157i		0		−8.65216	+	184.125i	631.848			71.8865	−	506.928i	−198.114				0
99.13	0.375512	−	7.99118i	−23.0410			−63.7180	−	6.00157i		0		−8.65216	+	184.125i	−631.848			−71.8865	+	506.928i	−198.114				0
99.14	0.375512	+	7.99118i	−23.0410			−63.7180	+	6.00157i		0		−8.65216	−	184.125i	−631.848			−71.8865	−	506.928i	−198.114				0
99.15	2.90251	−	7.45489i	−22.0610			−47.1509	−	43.2758i		0		−64.0322	+	164.462i	85.8808			−459.472	+	225.897i	−242.313				0
99.16	2.90251	+	7.45489i	−22.0610			−47.1509	+	43.2758i		0		−64.0322	−	164.462i	85.8808			−459.472	−	225.897i	−242.313				0
99.17	5.75952	−	5.55229i	49.8952			2.34412	−	63.9571i		0		287.372	−	277.032i	331.710			−341.607	−	381.377i	1760.53				0
99.18	5.75952	+	5.55229i	49.8952			2.34412	+	63.9571i		0		287.372	+	277.032i	331.710			−341.607	+	381.377i	1760.53				0
99.19	6.27431	−	4.96317i	26.0537			14.7338	−	62.2809i		0		163.469	−	129.309i	−195.627			−216.667	−	463.896i	−50.2058				0
99.20	6.27431	+	4.96317i	26.0537			14.7338	+	62.2809i		0		163.469	+	129.309i	−195.627			−216.667	+	463.896i	−50.2058				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.b	even	2	1	inner
20.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	100.7.d.c		24
4.b	odd	2	1	inner	100.7.d.c		24
5.b	even	2	1	inner	100.7.d.c		24
5.c	odd	4	1		100.7.b.e	✓	12
5.c	odd	4	1		100.7.b.g	yes	12
20.d	odd	2	1	inner	100.7.d.c		24
20.e	even	4	1		100.7.b.e	✓	12
20.e	even	4	1		100.7.b.g	yes	12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
100.7.b.e	✓	12	5.c	odd	4	1
100.7.b.e	✓	12	20.e	even	4	1
100.7.b.g	yes	12	5.c	odd	4	1
100.7.b.g	yes	12	20.e	even	4	1
100.7.d.c		24	1.a	even	1	1	trivial
100.7.d.c		24	4.b	odd	2	1	inner
100.7.d.c		24	5.b	even	2	1	inner
100.7.d.c		24	20.d	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^12 - 6062*T3^10 + 13083611*T3^8 - 12485415540*T3^6 + 5499458319015*T3^4 - 966823152954750*T3^2 + 25402876901020125