Newform orbit 429.2.m.a

• Label: 429.2.m.a
• Level: $429$
• Weight: $2$
• Character orbit: 429.m
• Analytic conductor: $3.426$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.42558224671\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
109.1	−1.92734	−	1.92734i	−1.00000					5.42931i	−1.59813	+	1.59813i	1.92734	+	1.92734i	−1.66792	+	1.66792i	6.60946	−	6.60946i	1.00000			6.16029
109.2	−1.67111	−	1.67111i	−1.00000					3.58521i	2.12568	−	2.12568i	1.67111	+	1.67111i	−1.37191	+	1.37191i	2.64907	−	2.64907i	1.00000			−7.10448
109.3	−1.12106	−	1.12106i	−1.00000					0.513571i	0.850971	−	0.850971i	1.12106	+	1.12106i	−0.675060	+	0.675060i	−1.66638	+	1.66638i	1.00000			−1.90799
109.4	−1.06339	−	1.06339i	−1.00000					0.261597i	0.340859	−	0.340859i	1.06339	+	1.06339i	−0.593196	+	0.593196i	−1.84860	+	1.84860i	1.00000			−0.724932
109.5	−0.735263	−	0.735263i	−1.00000				−	0.918776i	−2.75658	+	2.75658i	0.735263	+	0.735263i	−0.0552347	+	0.0552347i	−2.14607	+	2.14607i	1.00000			4.05362
109.6	−0.200229	−	0.200229i	−1.00000				−	1.91982i	−0.906673	+	0.906673i	0.200229	+	0.200229i	2.29691	−	2.29691i	−0.784861	+	0.784861i	1.00000			0.363084
109.7	−0.156364	−	0.156364i	−1.00000				−	1.95110i	2.94387	−	2.94387i	0.156364	+	0.156364i	3.04129	−	3.04129i	−0.617812	+	0.617812i	1.00000			−0.920633
109.8	0.156364	+	0.156364i	−1.00000				−	1.95110i	2.94387	−	2.94387i	−0.156364	−	0.156364i	−3.04129	+	3.04129i	0.617812	−	0.617812i	1.00000			0.920633
109.9	0.200229	+	0.200229i	−1.00000				−	1.91982i	−0.906673	+	0.906673i	−0.200229	−	0.200229i	−2.29691	+	2.29691i	0.784861	−	0.784861i	1.00000			−0.363084
109.10	0.735263	+	0.735263i	−1.00000				−	0.918776i	−2.75658	+	2.75658i	−0.735263	−	0.735263i	0.0552347	−	0.0552347i	2.14607	−	2.14607i	1.00000			−4.05362
109.11	1.06339	+	1.06339i	−1.00000					0.261597i	0.340859	−	0.340859i	−1.06339	−	1.06339i	0.593196	−	0.593196i	1.84860	−	1.84860i	1.00000			0.724932
109.12	1.12106	+	1.12106i	−1.00000					0.513571i	0.850971	−	0.850971i	−1.12106	−	1.12106i	0.675060	−	0.675060i	1.66638	−	1.66638i	1.00000			1.90799
109.13	1.67111	+	1.67111i	−1.00000					3.58521i	2.12568	−	2.12568i	−1.67111	−	1.67111i	1.37191	−	1.37191i	−2.64907	+	2.64907i	1.00000			7.10448
109.14	1.92734	+	1.92734i	−1.00000					5.42931i	−1.59813	+	1.59813i	−1.92734	−	1.92734i	1.66792	−	1.66792i	−6.60946	+	6.60946i	1.00000			−6.16029
307.1	−1.92734	+	1.92734i	−1.00000				−	5.42931i	−1.59813	−	1.59813i	1.92734	−	1.92734i	−1.66792	−	1.66792i	6.60946	+	6.60946i	1.00000			6.16029
307.2	−1.67111	+	1.67111i	−1.00000				−	3.58521i	2.12568	+	2.12568i	1.67111	−	1.67111i	−1.37191	−	1.37191i	2.64907	+	2.64907i	1.00000			−7.10448
307.3	−1.12106	+	1.12106i	−1.00000				−	0.513571i	0.850971	+	0.850971i	1.12106	−	1.12106i	−0.675060	−	0.675060i	−1.66638	−	1.66638i	1.00000			−1.90799
307.4	−1.06339	+	1.06339i	−1.00000				−	0.261597i	0.340859	+	0.340859i	1.06339	−	1.06339i	−0.593196	−	0.593196i	−1.84860	−	1.84860i	1.00000			−0.724932
307.5	−0.735263	+	0.735263i	−1.00000					0.918776i	−2.75658	−	2.75658i	0.735263	−	0.735263i	−0.0552347	−	0.0552347i	−2.14607	−	2.14607i	1.00000			4.05362
307.6	−0.200229	+	0.200229i	−1.00000					1.91982i	−0.906673	−	0.906673i	0.200229	−	0.200229i	2.29691	+	2.29691i	−0.784861	−	0.784861i	1.00000			0.363084

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
13.d	odd	4	1	inner
143.g	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	429.2.m.a	✓	28
11.b	odd	2	1	inner	429.2.m.a	✓	28
13.d	odd	4	1	inner	429.2.m.a	✓	28
143.g	even	4	1	inner	429.2.m.a	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
429.2.m.a	✓	28	1.a	even	1	1	trivial
429.2.m.a	✓	28	11.b	odd	2	1	inner
429.2.m.a	✓	28	13.d	odd	4	1	inner
429.2.m.a	✓	28	143.g	even	4	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{28} + 99T_{2}^{24} + 2857T_{2}^{20} + 25707T_{2}^{16} + 82143T_{2}^{12} + 65769T_{2}^{8} + 575T_{2}^{4} + 1 \) acting on \(S_{2}^{\mathrm{new}}(429, [\chi])\).