Newform orbit 968.2.q.b

• Label: 968.2.q.b
• Level: $968$
• Weight: $2$
• Character orbit: 968.q
• Analytic conductor: $7.730$
• Analytic rank: $0$
• Dimension: $170$
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$968 = 2^{3} \cdot 11^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	968.q (of order $11$, degree $10$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$170$
Relative dimension:	$17$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

$\operatorname{Tr}(f)(q) =$ 170 * q + 10 * q^3 - 3 * q^5 + 2 * q^7 + 180 * q^9 + 2 * q^11 + 3 * q^13 + 10 * q^15 - 6 * q^17 + 9 * q^19 + 16 * q^21 + 23 * q^23 - 18 * q^25 - 26 * q^27 + q^29 - 38 * q^31 + q^33 - 10 * q^35 - 24 * q^37 + 79 * q^39 - 4 * q^41 + 3 * q^43 - 37 * q^45 - 25 * q^47 - 39 * q^49 + 9 * q^51 + 17 * q^53 + 69 * q^55 + 63 * q^57 - 28 * q^59 + 34 * q^61 + 22 * q^63 + 84 * q^65 - 19 * q^67 - 12 * q^69 + 15 * q^71 - 46 * q^73 + 23 * q^75 + 108 * q^77 + 47 * q^79 + 226 * q^81 - 9 * q^83 - 8 * q^85 - 91 * q^87 - 100 * q^89 - 16 * q^91 - 6 * q^93 + 45 * q^95 + 18 * q^97 - 74 * 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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
89.1		0		−2.92790				0		−1.58795	−	3.47712i		0		−4.12052	+	2.64810i		0		5.57262				0
89.2		0		−2.74456				0		1.17344	+	2.56948i		0		0.111432	−	0.0716129i		0		4.53259				0
89.3		0		−2.73957				0		−0.663430	−	1.45271i		0		3.33076	−	2.14055i		0		4.50527				0
89.4		0		−2.73222				0		0.309747	+	0.678251i		0		−0.883657	+	0.567892i		0		4.46504				0
89.5		0		−1.05598				0		−0.502316	−	1.09992i		0		−0.0815169	+	0.0523877i		0		−1.88492				0
89.6		0		−1.03194				0		−0.0505481	−	0.110685i		0		−3.31366	+	2.12956i		0		−1.93511				0
89.7		0		−0.999400				0		0.729872	+	1.59820i		0		2.00590	−	1.28912i		0		−2.00120				0
89.8		0		−0.168615				0		−1.69959	−	3.72159i		0		1.53704	−	0.987794i		0		−2.97157				0
89.9		0		0.354731				0		1.80265	+	3.94726i		0		−3.77453	+	2.42574i		0		−2.87417				0
89.10		0		0.828920				0		0.388590	+	0.850894i		0		3.45207	−	2.21851i		0		−2.31289				0
89.11		0		0.899266				0		0.440967	+	0.965584i		0		−1.93013	+	1.24042i		0		−2.19132				0
89.12		0		1.24375				0		1.26032	+	2.75972i		0		1.83915	−	1.18195i		0		−1.45308				0
89.13		0		1.27915				0		−1.43170	−	3.13498i		0		−1.95916	+	1.25907i		0		−1.36377				0
89.14		0		2.00219				0		−0.684988	−	1.49991i		0		−0.643255	+	0.413395i		0		1.00878				0
89.15		0		2.63121				0		−0.954536	−	2.09014i		0		4.07705	−	2.62016i		0		3.92325				0
89.16		0		3.05084				0		1.06220	+	2.32589i		0		0.403770	−	0.259487i		0		6.30765				0
89.17		0		3.11012				0		0.0255015	+	0.0558405i		0		−3.53400	+	2.27116i		0		6.67282				0
177.1		0		−3.35746				0		0.195173	−	0.225241i		0		0.0423050	−	0.0926350i		0		8.27254				0
177.2		0		−2.74058				0		2.88694	−	3.33170i		0		0.227828	−	0.498874i		0		4.51077				0
177.3		0		−2.20507				0		−2.59828	+	2.99857i		0		1.82594	−	3.99824i		0		1.86234				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
121.e	even	11	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	968.2.q.b	✓	170
121.e	even	11	1	inner	968.2.q.b	✓	170

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
968.2.q.b	✓	170	1.a	even	1	1	trivial
968.2.q.b	✓	170	121.e	even	11	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^85 - 5*T3^84 - 160*T3^83 + 836*T3^82 + 12163*T3^81 - 66862*T3^80 - 583936*T3^79 + 3405876*T3^78 + 19842202*T3^77 - 124127579*T3^76 - 506529434*T3^75 + 3447017189*T3^74 + 10051450579*T3^73 - 75849200379*T3^72 - 157926412895*T3^71 + 1357807981713*T3^70 + 1974452596538*T3^69 - 20147044108284*T3^68 - 19391427717212*T3^67 + 251182878484058*T3^66 + 141961774690433*T3^65 - 2658089404143252*T3^64 - 625177633808502*T3^63 + 24055903027159464*T3^62 - 1100606432640423*T3^61 - 187218154629164530*T3^60 + 54440775422322946*T3^59 + 1257889072242342422*T3^58 - 641312093448454425*T3^57 - 7314619180647730426*T3^56 + 5200062355718126847*T3^55 + 36857918005308987725*T3^54 - 33212828173448201267*T3^53 - 160937147027946936803*T3^52 + 174991826085993713049*T3^51 + 608131055434978119408*T3^50 - 776749380716659768219*T3^49 - 1983013319837314883343*T3^48 + 2936144839311759000359*T3^47 + 5553559171144657753072*T3^46 - 9504461310451443529562*T3^45 - 13257229250955109680048*T3^44 + 26411836223761655196267*T3^43 + 26650620822836501482092*T3^42 - 63027516272622151707427*T3^41 - 44187940964468543561060*T3^40 + 128985506974408888918671*T3^39 + 58003072921332079750107*T3^38 - 225747511233457172729808*T3^37 - 54254129003740341215308*T3^36 + 336485966675066348955561*T3^35 + 21081894243097274413544*T3^34 - 424749810628363772033036*T3^33 + 38726035255229327499846*T3^32 + 450785943690124112806675*T3^31 - 102543513780942243216423*T3^30 - 398537086592537957468564*T3^29 + 140240661081274499940345*T3^28 + 290079274070594953057180*T3^27 - 136379371815859090137617*T3^26 - 171195986406887551682419*T3^25 + 100869419250249857816758*T3^24 + 80269210928530338251008*T3^23 - 57740699574616568642288*T3^22 - 29053046887611258095614*T3^21 + 25541177425616954607044*T3^20 + 7763467811692282575936*T3^19 - 8620508603853780118494*T3^18 - 1410508462088839605621*T3^17 + 2171597926208530296788*T3^16 + 139346904322733547738*T3^15 - 395267243270387214240*T3^14 + 1640384508965754361*T3^13 + 49654534240162601053*T3^12 - 2301366294810480039*T3^11 - 4038753423924607519*T3^10 + 261333435150877133*T3^9 + 195109659404578611*T3^8 - 12141829987045660*T3^7 - 4991049033329843*T3^6 + 262908996106757*T3^5 + 52987842720736*T3^4 - 3376257413232*T3^3 - 150536586816*T3^2 + 15089516288*T3 - 289676288