Newform orbit 100.11.d.c

• Label: 100.11.d.c
• Level: $100$
• Weight: $11$
• Character orbit: 100.d
• Analytic conductor: $63.536$
• Analytic rank: $0$
• Dimension: $40$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(63.5357252674\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Twist minimal:	no (minimal twist has level 20)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 1288 q^{4} - 29568 q^{6} + 829736 q^{9}+O(q^{10}) \)

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	−31.9907	−	0.770283i	−80.5620			1022.81	+	49.2838i		0		2577.24	+	62.0555i	−345.112			−32682.6	−	2364.48i	−52558.8				0
99.2	−31.9907	+	0.770283i	−80.5620			1022.81	−	49.2838i		0		2577.24	−	62.0555i	−345.112			−32682.6	+	2364.48i	−52558.8				0
99.3	−31.2124	−	7.05603i	−442.423			924.425	+	440.471i		0		13809.1	+	3121.75i	−2455.96			−25745.5	−	20270.9i	136689.				0
99.4	−31.2124	+	7.05603i	−442.423			924.425	−	440.471i		0		13809.1	−	3121.75i	−2455.96			−25745.5	+	20270.9i	136689.				0
99.5	−30.4011	−	9.98863i	330.781			824.454	+	607.331i		0		−10056.1	−	3304.05i	−29449.0			−18997.9	−	26698.7i	50366.8				0
99.6	−30.4011	+	9.98863i	330.781			824.454	−	607.331i		0		−10056.1	+	3304.05i	−29449.0			−18997.9	+	26698.7i	50366.8				0
99.7	−29.2335	−	13.0154i	448.707			685.197	+	760.974i		0		−13117.3	−	5840.12i	19334.7			−10126.3	−	31164.1i	142289.				0
99.8	−29.2335	+	13.0154i	448.707			685.197	−	760.974i		0		−13117.3	+	5840.12i	19334.7			−10126.3	+	31164.1i	142289.				0
99.9	−27.3833	−	16.5576i	17.1314			475.690	+	906.805i		0		−469.114	−	283.655i	−2883.30			1988.60	−	32707.6i	−58755.5				0
99.10	−27.3833	+	16.5576i	17.1314			475.690	−	906.805i		0		−469.114	+	283.655i	−2883.30			1988.60	+	32707.6i	−58755.5				0
99.11	−20.8647	−	24.2624i	−208.777			−153.329	+	1012.46i		0		4356.06	+	5065.43i	−17557.3			27763.8	−	17404.4i	−15461.2				0
99.12	−20.8647	+	24.2624i	−208.777			−153.329	−	1012.46i		0		4356.06	−	5065.43i	−17557.3			27763.8	+	17404.4i	−15461.2				0
99.13	−11.3585	−	29.9163i	137.165			−765.971	+	679.606i		0		−1557.98	−	4103.46i	−24910.8			29031.6	+	15195.7i	−40234.9				0
99.14	−11.3585	+	29.9163i	137.165			−765.971	−	679.606i		0		−1557.98	+	4103.46i	−24910.8			29031.6	−	15195.7i	−40234.9				0
99.15	−9.58811	−	30.5298i	321.971			−840.136	+	585.446i		0		−3087.10	−	9829.71i	−9880.78			25928.9	+	20035.9i	44616.5				0
99.16	−9.58811	+	30.5298i	321.971			−840.136	−	585.446i		0		−3087.10	+	9829.71i	−9880.78			25928.9	−	20035.9i	44616.5				0
99.17	−8.19968	−	30.9316i	−206.425			−889.530	+	507.259i		0		1692.62	+	6385.07i	1527.38			22984.2	+	23355.3i	−16437.6				0
99.18	−8.19968	+	30.9316i	−206.425			−889.530	−	507.259i		0		1692.62	−	6385.07i	1527.38			22984.2	−	23355.3i	−16437.6				0
99.19	−5.58516	−	31.5088i	275.626			−961.612	+	351.964i		0		−1539.42	−	8684.66i	19327.7			16460.7	+	28333.5i	16920.9				0
99.20	−5.58516	+	31.5088i	275.626			−961.612	−	351.964i		0		−1539.42	+	8684.66i	19327.7			16460.7	−	28333.5i	16920.9				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	100.11.d.c		40
4.b	odd	2	1	inner	100.11.d.c		40
5.b	even	2	1	inner	100.11.d.c		40
5.c	odd	4	1		20.11.b.a	✓	20
5.c	odd	4	1		100.11.b.e		20
15.e	even	4	1		180.11.c.a		20
20.d	odd	2	1	inner	100.11.d.c		40
20.e	even	4	1		20.11.b.a	✓	20
20.e	even	4	1		100.11.b.e		20
40.i	odd	4	1		320.11.b.d		20
40.k	even	4	1		320.11.b.d		20
60.l	odd	4	1		180.11.c.a		20

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
20.11.b.a	✓	20	5.c	odd	4	1
20.11.b.a	✓	20	20.e	even	4	1
100.11.b.e		20	5.c	odd	4	1
100.11.b.e		20	20.e	even	4	1
100.11.d.c		40	1.a	even	1	1	trivial
100.11.d.c		40	4.b	odd	2	1	inner
100.11.d.c		40	5.b	even	2	1	inner
100.11.d.c		40	20.d	odd	2	1	inner
180.11.c.a		20	15.e	even	4	1
180.11.c.a		20	60.l	odd	4	1
320.11.b.d		20	40.i	odd	4	1
320.11.b.d		20	40.k	even	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^20 - 797924*T3^18 + 262615424816*T3^16 - 46435851366897024*T3^14 + 4821651003865469342976*T3^12 - 301571240446873385039969280*T3^10 + 11187302635605863060647401000960*T3^8 - 231901938813815011164683747310796800*T3^6 + 2344243089583287569580334319316551270400*T3^4 - 8370092026305525697193120120638201036800000*T3^2 + 2260357211933581654165098764195295923404800000