Newform orbit 961.2.c.k

• Label: 961.2.c.k
• Level: $961$
• Weight: $2$
• Character orbit: 961.c
• Analytic conductor: $7.674$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$961 = 31^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-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 + 32 * q^4 - 8 * q^5 - 8 * q^7 + 24 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 - 32 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 - 12 * q^25 + 20 * q^28 + 48 * q^32 - 80 * q^33 + 112 * q^35 - 40 * q^36 - 36 * q^38 - 32 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 + 96 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 + 8 * q^56 - 40 * q^59 - 16 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 24 * q^69 + 24 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 - 208 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 - 64 * q^87 + 44 * q^90 + 32 * q^94 + 80 * q^95 - 16 * q^97 - 4 * q^98

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
439.1	−2.13825			−1.45242	+	2.51567i	2.57209			0.648062	+	1.12248i	3.10564	−	5.37913i	1.35517	−	2.34722i	−1.22328			−2.71907	−	4.70958i	−1.38572	−	2.40013i
439.2	−2.13825			1.45242	−	2.51567i	2.57209			0.648062	+	1.12248i	−3.10564	+	5.37913i	1.35517	−	2.34722i	−1.22328			−2.71907	−	4.70958i	−1.38572	−	2.40013i
439.3	−1.80264			−0.0954837	+	0.165383i	1.24951			1.23318	+	2.13593i	0.172123	−	0.298125i	0.526075	−	0.911189i	1.35286			1.48177	+	2.56649i	−2.22298	−	3.85032i
439.4	−1.80264			0.0954837	−	0.165383i	1.24951			1.23318	+	2.13593i	−0.172123	+	0.298125i	0.526075	−	0.911189i	1.35286			1.48177	+	2.56649i	−2.22298	−	3.85032i
439.5	−1.24512			−1.33932	+	2.31977i	−0.449667			−1.30938	−	2.26791i	1.66762	−	2.88840i	−0.602271	+	1.04316i	3.05014			−2.08754	−	3.61573i	1.63034	+	2.82383i
439.6	−1.24512			1.33932	−	2.31977i	−0.449667			−1.30938	−	2.26791i	−1.66762	+	2.88840i	−0.602271	+	1.04316i	3.05014			−2.08754	−	3.61573i	1.63034	+	2.82383i
439.7	0.720616			−0.949328	+	1.64428i	−1.48071			−1.39356	−	2.41371i	−0.684101	+	1.18490i	−2.10066	+	3.63846i	−2.50826			−0.302446	−	0.523851i	−1.00422	−	1.73936i
439.8	0.720616			0.949328	−	1.64428i	−1.48071			−1.39356	−	2.41371i	0.684101	−	1.18490i	−2.10066	+	3.63846i	−2.50826			−0.302446	−	0.523851i	−1.00422	−	1.73936i
439.9	1.96916			−0.810772	+	1.40430i	1.87757			−1.75290	−	3.03611i	−1.59654	+	2.76528i	−1.04579	+	1.81136i	−0.241077			0.185296	+	0.320943i	−3.45173	−	5.97857i
439.10	1.96916			0.810772	−	1.40430i	1.87757			−1.75290	−	3.03611i	1.59654	−	2.76528i	−1.04579	+	1.81136i	−0.241077			0.185296	+	0.320943i	−3.45173	−	5.97857i
439.11	2.49624			−1.23653	+	2.14173i	4.23120			0.574589	+	0.995217i	−3.08667	+	5.34626i	−0.132518	+	0.229528i	5.56961			−1.55800	−	2.69853i	1.43431	+	2.48430i
439.12	2.49624			1.23653	−	2.14173i	4.23120			0.574589	+	0.995217i	3.08667	−	5.34626i	−0.132518	+	0.229528i	5.56961			−1.55800	−	2.69853i	1.43431	+	2.48430i
521.1	−2.13825			−1.45242	−	2.51567i	2.57209			0.648062	−	1.12248i	3.10564	+	5.37913i	1.35517	+	2.34722i	−1.22328			−2.71907	+	4.70958i	−1.38572	+	2.40013i
521.2	−2.13825			1.45242	+	2.51567i	2.57209			0.648062	−	1.12248i	−3.10564	−	5.37913i	1.35517	+	2.34722i	−1.22328			−2.71907	+	4.70958i	−1.38572	+	2.40013i
521.3	−1.80264			−0.0954837	−	0.165383i	1.24951			1.23318	−	2.13593i	0.172123	+	0.298125i	0.526075	+	0.911189i	1.35286			1.48177	−	2.56649i	−2.22298	+	3.85032i
521.4	−1.80264			0.0954837	+	0.165383i	1.24951			1.23318	−	2.13593i	−0.172123	−	0.298125i	0.526075	+	0.911189i	1.35286			1.48177	−	2.56649i	−2.22298	+	3.85032i
521.5	−1.24512			−1.33932	−	2.31977i	−0.449667			−1.30938	+	2.26791i	1.66762	+	2.88840i	−0.602271	−	1.04316i	3.05014			−2.08754	+	3.61573i	1.63034	−	2.82383i
521.6	−1.24512			1.33932	+	2.31977i	−0.449667			−1.30938	+	2.26791i	−1.66762	−	2.88840i	−0.602271	−	1.04316i	3.05014			−2.08754	+	3.61573i	1.63034	−	2.82383i
521.7	0.720616			−0.949328	−	1.64428i	−1.48071			−1.39356	+	2.41371i	−0.684101	−	1.18490i	−2.10066	−	3.63846i	−2.50826			−0.302446	+	0.523851i	−1.00422	+	1.73936i
521.8	0.720616			0.949328	+	1.64428i	−1.48071			−1.39356	+	2.41371i	0.684101	+	1.18490i	−2.10066	−	3.63846i	−2.50826			−0.302446	+	0.523851i	−1.00422	+	1.73936i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
31.b	odd	2	1	inner
31.c	even	3	1	inner
31.e	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	961.2.c.k		24
31.b	odd	2	1	inner	961.2.c.k		24
31.c	even	3	1		961.2.a.k	✓	12
31.c	even	3	1	inner	961.2.c.k		24
31.d	even	5	4		961.2.g.v		96
31.e	odd	6	1		961.2.a.k	✓	12
31.e	odd	6	1	inner	961.2.c.k		24
31.f	odd	10	4		961.2.g.v		96
31.g	even	15	4		961.2.d.r		48
31.g	even	15	4		961.2.g.v		96
31.h	odd	30	4		961.2.d.r		48
31.h	odd	30	4		961.2.g.v		96
93.g	even	6	1		8649.2.a.bp		12
93.h	odd	6	1		8649.2.a.bp		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
961.2.a.k	✓	12	31.c	even	3	1
961.2.a.k	✓	12	31.e	odd	6	1
961.2.c.k		24	1.a	even	1	1	trivial
961.2.c.k		24	31.b	odd	2	1	inner
961.2.c.k		24	31.c	even	3	1	inner
961.2.c.k		24	31.e	odd	6	1	inner
961.2.d.r		48	31.g	even	15	4
961.2.d.r		48	31.h	odd	30	4
961.2.g.v		96	31.d	even	5	4
961.2.g.v		96	31.f	odd	10	4
961.2.g.v		96	31.g	even	15	4
961.2.g.v		96	31.h	odd	30	4
8649.2.a.bp		12	93.g	even	6	1
8649.2.a.bp		12	93.h	odd	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(961, [\chi])$:

$T_{2}^{6} - 10T_{2}^{4} - 2T_{2}^{3} + 28T_{2}^{2} + 8T_{2} - 17$

T3^24 + 28*T3^22 + 482*T3^20 + 5336*T3^18 + 43680*T3^16 + 259504*T3^14 + 1170824*T3^12 + 3796832*T3^10 + 9046800*T3^8 + 13623552*T3^6 + 12815872*T3^4 + 466944*T3^2 + 16384