Newform orbit 552.2.n.b

• Label: 552.2.n.b
• Level: $552$
• Weight: $2$
• Character orbit: 552.n
• Analytic conductor: $4.408$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.40774219157\)
Analytic rank:	\(0\)
Dimension:	\(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
91.1	−1.38507	−	0.285614i	−1.00000			1.83685	+	0.791193i	−2.03317			1.38507	+	0.285614i	1.21988			−2.31819	−	1.62049i	1.00000			2.81608	+	0.580701i
91.2	−1.38507	−	0.285614i	−1.00000			1.83685	+	0.791193i	2.03317			1.38507	+	0.285614i	−1.21988			−2.31819	−	1.62049i	1.00000			−2.81608	−	0.580701i
91.3	−1.38507	+	0.285614i	−1.00000			1.83685	−	0.791193i	−2.03317			1.38507	−	0.285614i	1.21988			−2.31819	+	1.62049i	1.00000			2.81608	−	0.580701i
91.4	−1.38507	+	0.285614i	−1.00000			1.83685	−	0.791193i	2.03317			1.38507	−	0.285614i	−1.21988			−2.31819	+	1.62049i	1.00000			−2.81608	+	0.580701i
91.5	−1.07870	−	0.914558i	−1.00000			0.327167	+	1.97306i	−3.32574			1.07870	+	0.914558i	−3.62001			1.45156	−	2.42754i	1.00000			3.58746	+	3.04158i
91.6	−1.07870	−	0.914558i	−1.00000			0.327167	+	1.97306i	3.32574			1.07870	+	0.914558i	3.62001			1.45156	−	2.42754i	1.00000			−3.58746	−	3.04158i
91.7	−1.07870	+	0.914558i	−1.00000			0.327167	−	1.97306i	−3.32574			1.07870	−	0.914558i	−3.62001			1.45156	+	2.42754i	1.00000			3.58746	−	3.04158i
91.8	−1.07870	+	0.914558i	−1.00000			0.327167	−	1.97306i	3.32574			1.07870	−	0.914558i	3.62001			1.45156	+	2.42754i	1.00000			−3.58746	+	3.04158i
91.9	−0.409868	−	1.35352i	−1.00000			−1.66402	+	1.10953i	−3.34475			0.409868	+	1.35352i	4.25021			2.18379	+	1.79751i	1.00000			1.37091	+	4.52717i
91.10	−0.409868	−	1.35352i	−1.00000			−1.66402	+	1.10953i	3.34475			0.409868	+	1.35352i	−4.25021			2.18379	+	1.79751i	1.00000			−1.37091	−	4.52717i
91.11	−0.409868	+	1.35352i	−1.00000			−1.66402	−	1.10953i	−3.34475			0.409868	−	1.35352i	4.25021			2.18379	−	1.79751i	1.00000			1.37091	−	4.52717i
91.12	−0.409868	+	1.35352i	−1.00000			−1.66402	−	1.10953i	3.34475			0.409868	−	1.35352i	−4.25021			2.18379	−	1.79751i	1.00000			−1.37091	+	4.52717i
91.13	0.409868	−	1.35352i	−1.00000			−1.66402	−	1.10953i	−0.901487			−0.409868	+	1.35352i	−1.56211			−2.18379	+	1.79751i	1.00000			−0.369491	+	1.22018i
91.14	0.409868	−	1.35352i	−1.00000			−1.66402	−	1.10953i	0.901487			−0.409868	+	1.35352i	1.56211			−2.18379	+	1.79751i	1.00000			0.369491	−	1.22018i
91.15	0.409868	+	1.35352i	−1.00000			−1.66402	+	1.10953i	−0.901487			−0.409868	−	1.35352i	−1.56211			−2.18379	−	1.79751i	1.00000			−0.369491	−	1.22018i
91.16	0.409868	+	1.35352i	−1.00000			−1.66402	+	1.10953i	0.901487			−0.409868	−	1.35352i	1.56211			−2.18379	−	1.79751i	1.00000			0.369491	+	1.22018i
91.17	1.07870	−	0.914558i	−1.00000			0.327167	−	1.97306i	−0.969269			−1.07870	+	0.914558i	−4.55308			−1.45156	−	2.42754i	1.00000			−1.04555	+	0.886452i
91.18	1.07870	−	0.914558i	−1.00000			0.327167	−	1.97306i	0.969269			−1.07870	+	0.914558i	4.55308			−1.45156	−	2.42754i	1.00000			1.04555	−	0.886452i
91.19	1.07870	+	0.914558i	−1.00000			0.327167	+	1.97306i	−0.969269			−1.07870	−	0.914558i	−4.55308			−1.45156	+	2.42754i	1.00000			−1.04555	−	0.886452i
91.20	1.07870	+	0.914558i	−1.00000			0.327167	+	1.97306i	0.969269			−1.07870	−	0.914558i	4.55308			−1.45156	+	2.42754i	1.00000			1.04555	+	0.886452i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.d	odd	2	1	inner
23.b	odd	2	1	inner
184.h	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	552.2.n.b	✓	24
4.b	odd	2	1		2208.2.n.b		24
8.b	even	2	1		2208.2.n.b		24
8.d	odd	2	1	inner	552.2.n.b	✓	24
23.b	odd	2	1	inner	552.2.n.b	✓	24
92.b	even	2	1		2208.2.n.b		24
184.e	odd	2	1		2208.2.n.b		24
184.h	even	2	1	inner	552.2.n.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
552.2.n.b	✓	24	1.a	even	1	1	trivial
552.2.n.b	✓	24	8.d	odd	2	1	inner
552.2.n.b	✓	24	23.b	odd	2	1	inner
552.2.n.b	✓	24	184.h	even	2	1	inner
2208.2.n.b		24	4.b	odd	2	1
2208.2.n.b		24	8.b	even	2	1
2208.2.n.b		24	92.b	even	2	1
2208.2.n.b		24	184.e	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{12} - 36T_{5}^{10} + 484T_{5}^{8} - 2976T_{5}^{6} + 8216T_{5}^{4} - 8736T_{5}^{2} + 3072 \) acting on \(S_{2}^{\mathrm{new}}(552, [\chi])\).