Newform orbit 43.2.g.a

• Label: 43.2.g.a
• Level: $43$
• Weight: $2$
• Character orbit: 43.g
• Analytic conductor: $0.343$
• Analytic rank: $0$
• Dimension: $36$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.343356728692\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Relative dimension:	\(3\) over \(\Q(\zeta_{21})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
9.1	−1.44188	−	1.80806i	2.66973	+	0.402397i	−0.745019	+	3.26414i	−2.09843	−	1.43068i	−3.12187	−	5.40724i	−1.09365	+	1.89425i	2.80884	−	1.35267i	4.09883	+	1.26432i	0.438918	+	5.85695i
9.2	−1.11243	−	1.39495i	−2.93359	−	0.442167i	−0.263330	+	1.15372i	−0.492700	−	0.335917i	2.64662	+	4.58409i	2.18154	−	3.77854i	−1.31271	+	0.632167i	5.54371	+	1.71001i	0.0795092	+	1.06098i
9.3	1.06016	+	1.32939i	−1.14296	−	0.172273i	−0.198316	+	0.868879i	−1.45700	−	0.993363i	−0.982695	−	1.70208i	−0.297283	+	0.514909i	1.69861	−	0.818009i	−1.59004	−	0.490464i	−0.224073	−	2.99004i
10.1	−0.483758	−	2.11948i	−0.240184	−	0.222858i	−2.45624	+	1.18286i	0.0260188	−	0.00392170i	−0.356153	+	0.616875i	1.56464	+	2.71003i	0.984367	+	1.23436i	−0.216168	−	2.88456i	−0.0208988	−	0.0532492i
10.2	0.188565	+	0.826155i	−0.0129300	−	0.0119973i	1.15496	−	0.556200i	−3.39819	+	0.512194i	0.00747346	−	0.0129444i	−0.134521	−	0.232998i	1.73398	+	2.17435i	−0.224167	−	2.99130i	−1.06393	−	2.71085i
10.3	0.581275	+	2.54673i	−1.40948	−	1.30780i	−4.34603	+	2.09294i	2.95419	−	0.445272i	2.51133	−	4.34976i	−0.339884	−	0.588696i	−4.59900	−	5.76696i	0.0520854	+	0.695032i	2.85118	+	7.26470i
13.1	−0.483758	+	2.11948i	−0.240184	+	0.222858i	−2.45624	−	1.18286i	0.0260188	+	0.00392170i	−0.356153	−	0.616875i	1.56464	−	2.71003i	0.984367	−	1.23436i	−0.216168	+	2.88456i	−0.0208988	+	0.0532492i
13.2	0.188565	−	0.826155i	−0.0129300	+	0.0119973i	1.15496	+	0.556200i	−3.39819	−	0.512194i	0.00747346	+	0.0129444i	−0.134521	+	0.232998i	1.73398	−	2.17435i	−0.224167	+	2.99130i	−1.06393	+	2.71085i
13.3	0.581275	−	2.54673i	−1.40948	+	1.30780i	−4.34603	−	2.09294i	2.95419	+	0.445272i	2.51133	+	4.34976i	−0.339884	+	0.588696i	−4.59900	+	5.76696i	0.0520854	−	0.695032i	2.85118	−	7.26470i
14.1	−2.05399	+	0.989151i	−0.239882	−	3.20100i	1.99349	−	2.49975i	−0.131558	+	0.0405802i	3.65898	+	6.33755i	0.934721	−	1.61898i	−0.607386	+	2.66113i	−7.22235	+	1.08859i	0.230079	−	0.213482i
14.2	−0.982954	+	0.473366i	0.109070	+	1.45544i	−0.504856	+	0.633069i	1.29085	−	0.398175i	−0.796166	−	1.37900i	−0.108163	+	0.187343i	0.682116	−	2.98855i	0.860089	−	0.129637i	−1.08036	+	1.00243i
14.3	0.993512	−	0.478450i	−0.0482746	−	0.644179i	−0.488828	+	0.612971i	−3.17479	+	0.979294i	−0.356169	−	0.616903i	1.23273	−	2.13515i	−0.683135	+	2.99301i	2.55386	−	0.384932i	−2.68565	+	2.49192i
15.1	−1.72039	+	2.15730i	−0.528255	+	1.34597i	−1.24917	−	5.47296i	0.0684907	+	0.913945i	−1.99486	−	3.45520i	−0.971539	+	1.68276i	8.98382	+	4.32638i	0.666571	+	0.618487i	−2.08949	−	1.42459i
15.2	−0.651405	+	0.816837i	0.922165	−	2.34964i	0.202149	+	0.885672i	−0.0373507	−	0.498411i	1.31857	+	2.28383i	−1.65334	+	2.86367i	−2.73775	−	1.31843i	−2.47126	−	2.29299i	0.431451	+	0.294158i
15.3	−0.0594739	+	0.0745779i	−0.863608	+	2.20044i	0.443017	+	1.94098i	−0.284956	−	3.80248i	−0.112742	−	0.195275i	1.30981	−	2.26866i	−0.342987	−	0.165174i	−1.89695	−	1.76011i	0.300528	+	0.204897i
17.1	−0.515822	−	2.25996i	1.28860	−	0.397480i	−3.03942	+	1.46371i	−1.48781	+	3.79089i	−1.56298	−	2.70715i	1.38920	−	2.40617i	1.98513	+	2.48927i	−0.976224	+	0.665578i	9.33472	+	1.40698i
17.2	−0.178150	−	0.780524i	−0.711521	+	0.219475i	1.22446	−	0.589667i	0.511972	−	1.30448i	0.298063	+	0.516260i	−2.37928	+	4.12103i	−1.67671	−	2.10253i	−2.02062	+	1.37764i	−1.10939	−	0.167213i
17.3	0.377390	+	1.65345i	−1.63701	+	0.504949i	−0.789549	+	0.380227i	0.140805	−	0.358765i	−1.45270	−	2.51615i	1.74586	−	3.02391i	1.18819	+	1.48995i	−0.0539035	+	0.0367508i	0.646339	+	0.0974200i
23.1	−1.72039	−	2.15730i	−0.528255	−	1.34597i	−1.24917	+	5.47296i	0.0684907	−	0.913945i	−1.99486	+	3.45520i	−0.971539	−	1.68276i	8.98382	−	4.32638i	0.666571	−	0.618487i	−2.08949	+	1.42459i
23.2	−0.651405	−	0.816837i	0.922165	+	2.34964i	0.202149	−	0.885672i	−0.0373507	+	0.498411i	1.31857	−	2.28383i	−1.65334	−	2.86367i	−2.73775	+	1.31843i	−2.47126	+	2.29299i	0.431451	−	0.294158i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
43.g	even	21	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	43.2.g.a	✓	36
3.b	odd	2	1		387.2.y.c		36
4.b	odd	2	1		688.2.bg.c		36
43.g	even	21	1	inner	43.2.g.a	✓	36
43.g	even	21	1		1849.2.a.n		18
43.h	odd	42	1		1849.2.a.o		18
129.o	odd	42	1		387.2.y.c		36
172.o	odd	42	1		688.2.bg.c		36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
43.2.g.a	✓	36	1.a	even	1	1	trivial
43.2.g.a	✓	36	43.g	even	21	1	inner
387.2.y.c		36	3.b	odd	2	1
387.2.y.c		36	129.o	odd	42	1
688.2.bg.c		36	4.b	odd	2	1
688.2.bg.c		36	172.o	odd	42	1
1849.2.a.n		18	43.g	even	21	1
1849.2.a.o		18	43.h	odd	42	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(43, [\chi])\).