Newform orbit 1100.2.q.a

• Label: 1100.2.q.a
• Level: $1100$
• Weight: $2$
• Character orbit: 1100.q
• Analytic conductor: $8.784$
• Analytic rank: $0$
• Dimension: $44$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.q (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.78354422234\)
Analytic rank:	\(0\)
Dimension:	\(44\)
Relative dimension:	\(11\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 44 * q - 2 * q^3 + 9 * q^5 - 13 * q^9 - 11 * q^11 - 22 * q^15 - 16 * q^17 + 10 * q^19 - 6 * q^21 + 4 * q^23 + 9 * q^25 + 34 * q^27 + 12 * q^29 + 6 * q^31 - 2 * q^33 - 20 * q^35 - 39 * q^37 - 4 * q^39 + 12 * q^41 - 4 * q^43 - q^45 + 15 * q^47 - 4 * q^49 - 30 * q^51 - 17 * q^53 - q^55 + 8 * q^57 + 28 * q^59 + 10 * q^61 - 20 * q^63 + 20 * q^65 + 23 * q^67 + 50 * q^69 + 11 * q^71 - 16 * q^73 + 3 * q^75 + 33 * q^79 + 6 * q^81 - 2 * q^83 - 61 * q^85 - 79 * q^87 - 9 * q^89 + 62 * q^91 + 110 * q^93 - 6 * q^95 + 9 * q^97 + 22 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
221.1		0		−2.17901	−	1.58314i		0		2.07774	−	0.826446i		0		−3.56245				0		1.31469	+	4.04621i		0
221.2		0		−2.04637	−	1.48677i		0		0.173593	−	2.22932i		0		0.255306				0		1.05007	+	3.23180i		0
221.3		0		−1.33815	−	0.972225i		0		2.15006	+	0.614203i		0		4.40339				0		−0.0816190	−	0.251198i		0
221.4		0		−0.777730	−	0.565054i		0		−1.44196	+	1.70902i		0		0.377198				0		−0.641473	−	1.97425i		0
221.5		0		−0.373969	−	0.271705i		0		−0.504438	−	2.17843i		0		−0.0769037				0		−0.861021	−	2.64995i		0
221.6		0		−0.111477	−	0.0809931i		0		0.841505	+	2.07168i		0		−2.73868				0		−0.921184	−	2.83511i		0
221.7		0		0.0311423	+	0.0226262i		0		−2.13996	−	0.648503i		0		4.41001				0		−0.926593	−	2.85176i		0
221.8		0		0.566896	+	0.411874i		0		2.23355	+	0.106003i		0		−2.46147				0		−0.775320	−	2.38619i		0
221.9		0		1.54876	+	1.12524i		0		−2.19621	−	0.420307i		0		−0.798349				0		0.205440	+	0.632278i		0
221.10		0		1.91254	+	1.38954i		0		2.00631	−	0.987278i		0		2.33679				0		0.799933	+	2.46194i		0
221.11		0		2.26737	+	1.64734i		0		−0.391167	+	2.20159i		0		−2.14485				0		1.50019	+	4.61710i		0
441.1		0		−1.01941	−	3.13741i		0		0.191725	+	2.22783i		0		2.28503				0		−6.37709	+	4.63323i		0
441.2		0		−0.731621	−	2.25170i		0		−1.04748	−	1.97555i		0		−3.85817				0		−2.10782	+	1.53142i		0
441.3		0		−0.723944	−	2.22807i		0		2.22952	−	0.171041i		0		−0.684824				0		−2.01315	+	1.46264i		0
441.4		0		−0.522204	−	1.60718i		0		−2.20429	+	0.375629i		0		2.48828				0		0.116723	−	0.0848043i		0
441.5		0		−0.190498	−	0.586291i		0		1.47383	−	1.68162i		0		4.34749				0		2.11960	−	1.53998i		0
441.6		0		−0.00542904	−	0.0167089i		0		1.76120	+	1.37774i		0		−4.52828				0		2.42680	−	1.76317i		0
441.7		0		0.315132	+	0.969877i		0		−0.0263836	+	2.23591i		0		1.63581				0		1.58570	−	1.15208i		0
441.8		0		0.450092	+	1.38524i		0		1.03836	−	1.98035i		0		−0.487750				0		0.710744	−	0.516386i		0
441.9		0		0.551379	+	1.69697i		0		−1.42788	−	1.72080i		0		1.19730				0		−0.148634	+	0.107989i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
25.d	even	5	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1100.2.q.a	✓	44
25.d	even	5	1	inner	1100.2.q.a	✓	44

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1100.2.q.a	✓	44	1.a	even	1	1	trivial
1100.2.q.a	✓	44	25.d	even	5	1	inner