Newform orbit 148.3.m.a

• Label: 148.3.m.a
• Level: $148$
• Weight: $3$
• Character orbit: 148.m
• Analytic conductor: $4.033$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 148 = 2^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	148.m (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.03270791253\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(7\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 6 q^{5} + 44 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
29.1		0		−4.50093	−	2.59862i		0		−1.64484	−	6.13864i		0		−1.98273	+	3.43418i		0		9.00561	+	15.5982i		0
29.2		0		−3.28429	−	1.89619i		0		1.80218	+	6.72582i		0		5.52553	−	9.57050i		0		2.69104	+	4.66102i		0
29.3		0		−1.30131	−	0.751313i		0		−0.351990	−	1.31364i		0		−0.251745	+	0.436035i		0		−3.37106	−	5.83884i		0
29.4		0		−0.776009	−	0.448029i		0		1.24515	+	4.64696i		0		−3.59684	+	6.22991i		0		−4.09854	−	7.09888i		0
29.5		0		1.52917	+	0.882870i		0		−2.18102	−	8.13967i		0		1.48425	−	2.57080i		0		−2.94108	−	5.09410i		0
29.6		0		3.42511	+	1.97749i		0		0.805413	+	3.00584i		0		6.73037	−	11.6573i		0		3.32091	+	5.75199i		0
29.7		0		4.04224	+	2.33379i		0		0.557164	+	2.07937i		0		−5.31077	+	9.19852i		0		6.39312	+	11.0732i		0
45.1		0		−4.98945	−	2.88066i		0		−3.47957	+	0.932348i		0		−0.263363	+	0.456158i		0		12.0964	+	20.9516i		0
45.2		0		−1.85896	−	1.07327i		0		7.19156	−	1.92697i		0		−1.95032	+	3.37805i		0		−2.19618	−	3.80390i		0
45.3		0		−1.31198	−	0.757473i		0		−2.18286	+	0.584896i		0		−3.33581	+	5.77779i		0		−3.35247	−	5.80665i		0
45.4		0		−0.666132	−	0.384592i		0		−4.40092	+	1.17922i		0		2.98963	−	5.17820i		0		−4.20418	−	7.28185i		0
45.5		0		2.12559	+	1.22721i		0		1.95694	−	0.524360i		0		6.05298	−	10.4841i		0		−1.48790	−	2.57713i		0
45.6		0		3.57476	+	2.06389i		0		−7.54934	+	2.02284i		0		−4.49524	+	7.78599i		0		4.01929	+	6.96161i		0
45.7		0		3.99219	+	2.30489i		0		5.23215	−	1.40195i		0		−1.59596	+	2.76428i		0		6.12505	+	10.6089i		0
97.1		0		−4.50093	+	2.59862i		0		−1.64484	+	6.13864i		0		−1.98273	−	3.43418i		0		9.00561	−	15.5982i		0
97.2		0		−3.28429	+	1.89619i		0		1.80218	−	6.72582i		0		5.52553	+	9.57050i		0		2.69104	−	4.66102i		0
97.3		0		−1.30131	+	0.751313i		0		−0.351990	+	1.31364i		0		−0.251745	−	0.436035i		0		−3.37106	+	5.83884i		0
97.4		0		−0.776009	+	0.448029i		0		1.24515	−	4.64696i		0		−3.59684	−	6.22991i		0		−4.09854	+	7.09888i		0
97.5		0		1.52917	−	0.882870i		0		−2.18102	+	8.13967i		0		1.48425	+	2.57080i		0		−2.94108	+	5.09410i		0
97.6		0		3.42511	−	1.97749i		0		0.805413	−	3.00584i		0		6.73037	+	11.6573i		0		3.32091	−	5.75199i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
37.g	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	148.3.m.a	✓	28
37.g	odd	12	1	inner	148.3.m.a	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
148.3.m.a	✓	28	1.a	even	1	1	trivial
148.3.m.a	✓	28	37.g	odd	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(148, [\chi])\).