Newform orbit 3483.2.a.v

• Label: 3483.2.a.v
• Level: $3483$
• Weight: $2$
• Character orbit: 3483.a
• Self dual: yes
• Analytic conductor: $27.812$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3483 = 3^{4} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3483.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(27.8118950240\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 28 q^{4} + 8 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1.1	−2.63839				0		4.96112			−1.10617				0		1.72679			−7.81260				0		2.91850
1.2	−2.60148				0		4.76770			4.38978				0		−1.92656			−7.20013				0		−11.4199
1.3	−2.56445				0		4.57640			−0.224605				0		3.32871			−6.60706				0		0.575989
1.4	−2.34203				0		3.48509			−3.51183				0		−2.76798			−3.47811				0		8.22480
1.5	−1.92564				0		1.70809			−4.18643				0		4.92570			0.562110				0		8.06157
1.6	−1.64097				0		0.692794			2.32259				0		−2.67888			2.14509				0		−3.81131
1.7	−1.60554				0		0.577765			−1.37654				0		3.35515			2.28346				0		2.21009
1.8	−1.07822				0		−0.837451			0.354230				0		−4.34119			3.05938				0		−0.381937
1.9	−0.905504				0		−1.18006			−3.00518				0		−3.71133			2.87956				0		2.72120
1.10	−0.873052				0		−1.23778			−2.69461				0		0.260315			2.82675				0		2.35254
1.11	−0.615321				0		−1.62138			3.44505				0		3.22341			2.22831				0		−2.11981
1.12	−0.328186				0		−1.89229			1.01065				0		2.60587			1.27739				0		−0.331681
1.13	0.328186				0		−1.89229			−1.01065				0		2.60587			−1.27739				0		−0.331681
1.14	0.615321				0		−1.62138			−3.44505				0		3.22341			−2.22831				0		−2.11981
1.15	0.873052				0		−1.23778			2.69461				0		0.260315			−2.82675				0		2.35254
1.16	0.905504				0		−1.18006			3.00518				0		−3.71133			−2.87956				0		2.72120
1.17	1.07822				0		−0.837451			−0.354230				0		−4.34119			−3.05938				0		−0.381937
1.18	1.60554				0		0.577765			1.37654				0		3.35515			−2.28346				0		2.21009
1.19	1.64097				0		0.692794			−2.32259				0		−2.67888			−2.14509				0		−3.81131
1.20	1.92564				0		1.70809			4.18643				0		4.92570			−0.562110				0		8.06157

Atkin-Lehner signs

\( p \)	Sign
\(3\)	\( -1 \)
\(43\)	\( +1 \)

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3483.2.a.v	✓	24
3.b	odd	2	1	inner	3483.2.a.v	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3483.2.a.v	✓	24	1.a	even	1	1	trivial
3483.2.a.v	✓	24	3.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3483))\):

T2^24 - 38*T2^22 + 623*T2^20 - 5779*T2^18 + 33461*T2^16 - 126033*T2^14 + 312805*T2^12 - 508456*T2^10 + 529276*T2^8 - 338560*T2^6 + 123424*T2^4 - 21996*T2^2 + 1296

T5^24 - 87*T5^22 + 3214*T5^20 - 65908*T5^18 + 823189*T5^16 - 6465960*T5^14 + 31861992*T5^12 - 95592104*T5^10 + 165216852*T5^8 - 152381068*T5^6 + 64447360*T5^4 - 8080384*T5^2 + 262144