Newform orbit 124.3.o.a

• Label: 124.3.o.a
• Level: $124$
• Weight: $3$
• Character orbit: 124.o
• Analytic conductor: $3.379$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	124.o (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.37875527807\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(5\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1		0		−2.39545	−	5.38028i		0		−3.34056	−	5.78602i		0		5.42242	+	6.02221i		0		−17.1870	+	19.0881i		0
13.2		0		−1.21706	−	2.73355i		0		4.66965	+	8.08807i		0		2.28779	+	2.54085i		0		0.0310810	−	0.0345190i		0
13.3		0		−0.282508	−	0.634523i		0		−1.46593	−	2.53906i		0		−4.75907	−	5.28548i		0		5.69937	−	6.32979i		0
13.4		0		0.684837	+	1.53817i		0		−1.53767	−	2.66333i		0		8.16234	+	9.06519i		0		4.12521	−	4.58151i		0
13.5		0		1.73203	+	3.89021i		0		1.98810	+	3.44350i		0		−1.12705	−	1.25172i		0		−6.11161	+	6.78763i		0
17.1		0		−3.24569	−	2.92243i		0		−2.16722	+	3.75373i		0		−0.282561	+	2.68839i		0		1.05314	+	10.0199i		0
17.2		0		−1.31136	−	1.18075i		0		2.72362	−	4.71744i		0		−0.568373	+	5.40771i		0		−0.615273	−	5.85393i		0
17.3		0		−0.812474	−	0.731555i		0		0.0996144	−	0.172537i		0		0.900672	−	8.56932i		0		−0.815815	−	7.76196i		0
17.4		0		2.63052	+	2.36853i		0		−1.84144	+	3.18946i		0		−0.655396	+	6.23568i		0		0.368941	+	3.51024i		0
17.5		0		3.15255	+	2.83857i		0		4.11986	−	7.13581i		0		1.01453	−	9.65264i		0		0.940339	+	8.94673i		0
21.1		0		−4.90821	+	0.515874i		0		−1.45470	−	2.51962i		0		7.26879	+	1.54503i		0		15.0211	−	3.19283i		0
21.2		0		−2.43523	+	0.255953i		0		1.56711	+	2.71432i		0		−7.68423	−	1.63333i		0		−2.93848	+	0.624593i		0
21.3		0		−0.0268627	+	0.00282338i		0		−4.16141	−	7.20777i		0		0.359013	+	0.0763106i		0		−8.80261	+	1.87105i		0
21.4		0		2.04697	−	0.215145i		0		2.65148	+	4.59249i		0		3.34611	+	0.711237i		0		−4.65955	+	0.990417i		0
21.5		0		5.49247	−	0.577282i		0		−1.34312	−	2.32635i		0		0.977169	+	0.207704i		0		21.0307	−	4.47021i		0
53.1		0		−1.10618	+	5.20417i		0		1.56007	+	2.70213i		0		−1.90607	+	0.848638i		0		−17.6379	−	7.85289i		0
53.2		0		−0.357501	+	1.68191i		0		−4.52206	−	7.83243i		0		−12.1470	+	5.40819i		0		5.52090	+	2.45806i		0
53.3		0		−0.257314	+	1.21057i		0		−1.69238	−	2.93128i		0		9.33225	−	4.15499i		0		6.82265	+	3.03764i		0
53.4		0		0.177793	−	0.836450i		0		3.54343	+	6.13740i		0		−3.95326	+	1.76010i		0		7.55387	+	3.36320i		0
53.5		0		0.938675	−	4.41612i		0		−0.896461	−	1.55272i		0		3.51190	−	1.56360i		0		−10.3991	−	4.62997i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
31.h	odd	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	124.3.o.a	✓	40
31.h	odd	30	1	inner	124.3.o.a	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
124.3.o.a	✓	40	1.a	even	1	1	trivial
124.3.o.a	✓	40	31.h	odd	30	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(124, [\chi])\).