Newform orbit 1100.2.q.b

• Label: 1100.2.q.b
• Level: $1100$
• Weight: $2$
• Character orbit: 1100.q
• Analytic conductor: $8.784$
• Analytic rank: $0$
• Dimension: $52$
• 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:	$52$
Relative dimension:	$13$ 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.

$\operatorname{Tr}(f)(q) =$ 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * 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		−2.46992	−	1.79450i		0		−0.932128	−	2.03252i		0		4.85051				0		1.95322	+	6.01139i		0
221.2		0		−1.98827	−	1.44456i		0		1.83057	+	1.28413i		0		0.715669				0		0.939404	+	2.89119i		0
221.3		0		−1.84339	−	1.33930i		0		0.702061	+	2.12300i		0		−3.98140				0		0.677309	+	2.08454i		0
221.4		0		−1.67142	−	1.21436i		0		−1.73889	+	1.40580i		0		1.74835				0		0.391935	+	1.20625i		0
221.5		0		−1.19952	−	0.871501i		0		1.53725	−	1.62384i		0		0.464093				0		−0.247722	−	0.762409i		0
221.6		0		−0.463412	−	0.336688i		0		−1.34725	−	1.78463i		0		−3.78473				0		−0.825660	−	2.54112i		0
221.7		0		0.287074	+	0.208571i		0		1.90283	−	1.17441i		0		−3.22759				0		−0.888142	−	2.73342i		0
221.8		0		0.722709	+	0.525079i		0		1.39423	+	1.74818i		0		1.78111				0		−0.680451	−	2.09421i		0
221.9		0		0.921658	+	0.669624i		0		−1.47725	+	1.67861i		0		−4.58549				0		−0.525993	−	1.61884i		0
221.10		0		1.10560	+	0.803263i		0		0.235915	−	2.22359i		0		3.63293				0		−0.349938	−	1.07700i		0
221.11		0		1.36589	+	0.992379i		0		−2.23514	−	0.0642463i		0		0.0719347				0		−0.0462056	−	0.142206i		0
221.12		0		2.51887	+	1.83006i		0		1.68514	+	1.46980i		0		1.24095				0		2.06850	+	6.36620i		0
221.13		0		2.71414	+	1.97194i		0		−1.74832	−	1.39405i		0		1.07366				0		2.55096	+	7.85106i		0
441.1		0		−0.994170	−	3.05974i		0		0.246812	−	2.22240i		0		3.71818				0		−5.94659	+	4.32045i		0
441.2		0		−0.885916	−	2.72657i		0		−2.22917	−	0.175548i		0		−1.14570				0		−4.22229	+	3.06767i		0
441.3		0		−0.631762	−	1.94436i		0		1.75484	+	1.38583i		0		1.39297				0		−0.954372	+	0.693392i		0
441.4		0		−0.611345	−	1.88153i		0		−0.0494719	+	2.23552i		0		−3.07794				0		−0.739349	+	0.537169i		0
441.5		0		−0.183465	−	0.564647i		0		−1.90569	+	1.16976i		0		−0.847663				0		2.14188	−	1.55617i		0
441.6		0		−0.0542729	−	0.167035i		0		−1.54766	−	1.61392i		0		3.08318				0		2.40210	−	1.74522i		0
441.7		0		−0.0181419	−	0.0558349i		0		−0.144597	−	2.23139i		0		−1.97462				0		2.42426	−	1.76133i		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.b	✓	52
25.d	even	5	1	inner	1100.2.q.b	✓	52

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1100.2.q.b	✓	52	1.a	even	1	1	trivial
1100.2.q.b	✓	52	25.d	even	5	1	inner