Newform orbit 1375.4.a.g

• Label: 1375.4.a.g
• Level: $1375$
• Weight: $4$
• Character orbit: 1375.a
• Self dual: yes
• Analytic conductor: $81.128$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1375 = 5^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1375.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(81.1276262579\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	yes
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 112 q^{4} - 2 q^{6} + 392 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1.1	−5.53899			2.54820			22.6804				0		−14.1144			−14.7556			−81.3144			−20.5067				0
1.2	−5.05392			4.50167			17.5421				0		−22.7511			−10.4972			−48.2252			−6.73499				0
1.3	−4.90873			−8.95851			16.0956				0		43.9749			2.38710			−39.7391			53.2549				0
1.4	−4.84230			−8.63018			15.4479				0		41.7899			−26.3681			−36.0648			47.4799				0
1.5	−4.38606			6.87484			11.2375				0		−30.1534			22.7721			−14.1999			20.2634				0
1.6	−3.50428			4.84372			4.27999				0		−16.9738			−24.7280			13.0360			−3.53839				0
1.7	−3.39243			−5.06415			3.50859				0		17.1798			4.42548			15.2368			−1.35440				0
1.8	−3.20061			10.3084			2.24389				0		−32.9932			5.71808			18.4231			79.2637				0
1.9	−3.04931			−1.31977			1.29830				0		4.02440			14.6848			20.4356			−25.2582				0
1.10	−2.83685			1.65506			0.0476956				0		−4.69514			34.1360			22.5595			−24.2608				0
1.11	−2.10533			2.70952			−3.56758				0		−5.70443			−23.7277			24.3536			−19.6585				0
1.12	−1.32945			4.25140			−6.23255				0		−5.65204			0.00339340			18.9215			−8.92559				0
1.13	−1.22149			−6.72964			−6.50795				0		8.22022			24.9090			17.7214			18.2881				0
1.14	−0.998141			−8.98386			−7.00371				0		8.96716			−34.9238			14.9758			53.7097				0
1.15	−0.712128			−9.13874			−7.49287				0		6.50795			2.84777			11.0329			56.5165				0
1.16	−0.650174			−2.11216			−7.57727				0		1.37327			−1.62369			10.1279			−22.5388				0
1.17	0.650174			2.11216			−7.57727				0		1.37327			1.62369			−10.1279			−22.5388				0
1.18	0.712128			9.13874			−7.49287				0		6.50795			−2.84777			−11.0329			56.5165				0
1.19	0.998141			8.98386			−7.00371				0		8.96716			34.9238			−14.9758			53.7097				0
1.20	1.22149			6.72964			−6.50795				0		8.22022			−24.9090			−17.7214			18.2881				0

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\(1\)
\(11\)	\(1\)

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1375.4.a.g	✓	32
5.b	even	2	1	inner	1375.4.a.g	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1375.4.a.g	✓	32	1.a	even	1	1	trivial
1375.4.a.g	✓	32	5.b	even	2	1	inner