Newform orbit 931.2.bt.a

• Label: 931.2.bt.a
• Level: $931$
• Weight: $2$
• Character orbit: 931.bt
• Analytic conductor: $7.434$
• Analytic rank: $0$
• Dimension: $24$
• CM discriminant: -19
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.bt (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.43407242818\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(2\) over \(\Q(\zeta_{42})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{42}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 4 q^{4} + 3 q^{5} - 3 q^{7} - 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
75.1		0			0		−1.97766	−	0.298085i	−2.83032	+	3.05035i		0		−0.382824	+	2.61791i		0		−2.47872	+	1.68996i		0
75.2		0			0		−1.97766	−	0.298085i	3.03306	−	3.26887i		0		2.58198	−	0.577390i		0		−2.47872	+	1.68996i		0
94.1		0			0		0.730682	+	1.86175i	−0.743773	−	2.41125i		0		−0.790955	+	2.52476i		0		−0.224190	−	2.99161i		0
94.2		0			0		0.730682	+	1.86175i	0.195013	+	0.632217i		0		−2.07576	−	1.64049i		0		−0.224190	−	2.99161i		0
208.1		0			0		0.730682	−	1.86175i	−0.743773	+	2.41125i		0		−0.790955	−	2.52476i		0		−0.224190	+	2.99161i		0
208.2		0			0		0.730682	−	1.86175i	0.195013	−	0.632217i		0		−2.07576	+	1.64049i		0		−0.224190	+	2.99161i		0
341.1		0			0		1.65248	+	1.12664i	−0.452816	−	3.00424i		0		1.80808	+	1.93154i		0		2.19916	+	2.04052i		0
341.2		0			0		1.65248	+	1.12664i	0.620733	+	4.11829i		0		1.15842	−	2.37867i		0		2.19916	+	2.04052i		0
360.1		0			0		−1.97766	+	0.298085i	−2.83032	−	3.05035i		0		−0.382824	−	2.61791i		0		−2.47872	−	1.68996i		0
360.2		0			0		−1.97766	+	0.298085i	3.03306	+	3.26887i		0		2.58198	+	0.577390i		0		−2.47872	−	1.68996i		0
474.1		0			0		−1.46610	+	1.36035i	−2.18313	−	3.20207i		0		−2.46709	−	0.955766i		0		2.96649	−	0.447127i		0
474.2		0			0		−1.46610	+	1.36035i	1.41682	+	2.07809i		0		−0.0116306	+	2.64573i		0		2.96649	−	0.447127i		0
493.1		0			0		−1.46610	−	1.36035i	−2.18313	+	3.20207i		0		−2.46709	+	0.955766i		0		2.96649	+	0.447127i		0
493.2		0			0		−1.46610	−	1.36035i	1.41682	−	2.07809i		0		−0.0116306	−	2.64573i		0		2.96649	+	0.447127i		0
626.1		0			0		0.149460	−	1.99441i	0.625047	+	0.245313i		0		1.48078	+	2.19255i		0		−2.86672	+	0.884266i		0
626.2		0			0		0.149460	−	1.99441i	1.23149	+	0.483326i		0		−2.57680	+	0.600068i		0		−2.86672	+	0.884266i		0
740.1		0			0		1.91115	−	0.589510i	−3.85967	−	0.289242i		0		2.06126	+	1.65868i		0		−1.09602	−	2.79262i		0
740.2		0			0		1.91115	−	0.589510i	4.44753	+	0.333296i		0		−2.28545	+	1.33294i		0		−1.09602	−	2.79262i		0
759.1		0			0		1.65248	−	1.12664i	−0.452816	+	3.00424i		0		1.80808	−	1.93154i		0		2.19916	−	2.04052i		0
759.2		0			0		1.65248	−	1.12664i	0.620733	−	4.11829i		0		1.15842	+	2.37867i		0		2.19916	−	2.04052i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.b	odd	2	1	CM by \(\Q(\sqrt{-19}) \)
49.h	odd	42	1	inner
931.bt	even	42	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	931.2.bt.a	✓	24
19.b	odd	2	1	CM	931.2.bt.a	✓	24
49.h	odd	42	1	inner	931.2.bt.a	✓	24
931.bt	even	42	1	inner	931.2.bt.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
931.2.bt.a	✓	24	1.a	even	1	1	trivial
931.2.bt.a	✓	24	19.b	odd	2	1	CM
931.2.bt.a	✓	24	49.h	odd	42	1	inner
931.2.bt.a	✓	24	931.bt	even	42	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{2}^{\mathrm{new}}(931, [\chi])\).