Newform orbit 1476.2.c.a

• Label: 1476.2.c.a
• Level: $1476$
• Weight: $2$
• Character orbit: 1476.c
• Analytic conductor: $11.786$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1476.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.7859193383\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80 q + 8 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
575.1	−1.41394	−	0.0277941i		0		1.99845	+	0.0785985i			1.74371i		0				0.754192i	−2.82351	−	0.166679i		0		0.0484648	−	2.46550i
575.2	−1.41394	+	0.0277941i		0		1.99845	−	0.0785985i		−	1.74371i		0			−	0.754192i	−2.82351	+	0.166679i		0		0.0484648	+	2.46550i
575.3	−1.38924	−	0.264580i		0		1.85999	+	0.735133i		−	2.38168i		0				1.32875i	−2.38948	−	1.51340i		0		−0.630147	+	3.30874i
575.4	−1.38924	+	0.264580i		0		1.85999	−	0.735133i			2.38168i		0			−	1.32875i	−2.38948	+	1.51340i		0		−0.630147	−	3.30874i
575.5	−1.38734	−	0.274393i		0		1.84942	+	0.761353i			1.54163i		0			−	4.23948i	−2.35686	−	1.56372i		0		0.423014	−	2.13877i
575.6	−1.38734	+	0.274393i		0		1.84942	−	0.761353i		−	1.54163i		0				4.23948i	−2.35686	+	1.56372i		0		0.423014	+	2.13877i
575.7	−1.36717	−	0.361743i		0		1.73828	+	0.989124i		−	0.272560i		0			−	2.15427i	−2.01871	−	1.98111i		0		−0.0985966	+	0.372635i
575.8	−1.36717	+	0.361743i		0		1.73828	−	0.989124i			0.272560i		0				2.15427i	−2.01871	+	1.98111i		0		−0.0985966	−	0.372635i
575.9	−1.33412	−	0.469187i		0		1.55973	+	1.25190i			3.03471i		0				0.0550577i	−1.49348	−	2.40198i		0		1.42385	−	4.04865i
575.10	−1.33412	+	0.469187i		0		1.55973	−	1.25190i		−	3.03471i		0			−	0.0550577i	−1.49348	+	2.40198i		0		1.42385	+	4.04865i
575.11	−1.28510	−	0.590347i		0		1.30298	+	1.51731i		−	4.18926i		0			−	3.41832i	−0.778726	−	2.71911i		0		−2.47311	+	5.38363i
575.12	−1.28510	+	0.590347i		0		1.30298	−	1.51731i			4.18926i		0				3.41832i	−0.778726	+	2.71911i		0		−2.47311	−	5.38363i
575.13	−1.24246	−	0.675489i		0		1.08743	+	1.67854i			2.02392i		0				4.11689i	−0.217255	−	2.82007i		0		1.36713	−	2.51464i
575.14	−1.24246	+	0.675489i		0		1.08743	−	1.67854i		−	2.02392i		0			−	4.11689i	−0.217255	+	2.82007i		0		1.36713	+	2.51464i
575.15	−1.22008	−	0.715123i		0		0.977197	+	1.74502i			1.71240i		0				3.28993i	0.0556428	−	2.82788i		0		1.22458	−	2.08926i
575.16	−1.22008	+	0.715123i		0		0.977197	−	1.74502i		−	1.71240i		0			−	3.28993i	0.0556428	+	2.82788i		0		1.22458	+	2.08926i
575.17	−1.21141	−	0.729716i		0		0.935031	+	1.76797i		−	3.60459i		0				4.02059i	0.157409	−	2.82404i		0		−2.63033	+	4.36664i
575.18	−1.21141	+	0.729716i		0		0.935031	−	1.76797i			3.60459i		0			−	4.02059i	0.157409	+	2.82404i		0		−2.63033	−	4.36664i
575.19	−1.12259	−	0.860115i		0		0.520406	+	1.93111i		−	1.78065i		0			−	2.27215i	1.07677	−	2.61545i		0		−1.53156	+	1.99893i
575.20	−1.12259	+	0.860115i		0		0.520406	−	1.93111i			1.78065i		0				2.27215i	1.07677	+	2.61545i		0		−1.53156	−	1.99893i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1476.2.c.a	✓	80
3.b	odd	2	1	inner	1476.2.c.a	✓	80
4.b	odd	2	1	inner	1476.2.c.a	✓	80
12.b	even	2	1	inner	1476.2.c.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1476.2.c.a	✓	80	1.a	even	1	1	trivial
1476.2.c.a	✓	80	3.b	odd	2	1	inner
1476.2.c.a	✓	80	4.b	odd	2	1	inner
1476.2.c.a	✓	80	12.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1476, [\chi])\).