Newform orbit 795.2.m.a

• Label: 795.2.m.a
• Level: $795$
• Weight: $2$
• Character orbit: 795.m
• Analytic conductor: $6.348$
• Analytic rank: $0$
• Dimension: $40$
• CM discriminant: -159
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 795 = 3 \cdot 5 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	795.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.34810696069\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 160 q^{16} + 240 q^{36} + 20 q^{40} + 60 q^{42} - 140 q^{52} - 180 q^{60} + 220 q^{70} - 360 q^{81} + 260 q^{82}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
158.1	−1.96968	+	1.96968i	−1.22474	−	1.22474i		−	5.75926i	2.19865	+	0.407360i	4.82471			2.79770	−	2.79770i	7.40454	+	7.40454i			3.00000i	−5.13300	+	3.52826i
158.2	−1.96968	+	1.96968i	1.22474	+	1.22474i		−	5.75926i	−0.407360	−	2.19865i	−4.82471			2.48452	−	2.48452i	7.40454	+	7.40454i			3.00000i	5.13300	+	3.52826i
158.3	−1.79743	+	1.79743i	−1.22474	−	1.22474i		−	4.46151i	−1.96516	+	1.06684i	4.40279			−0.365573	+	0.365573i	4.42439	+	4.42439i			3.00000i	1.61466	−	5.44981i
158.4	−1.79743	+	1.79743i	1.22474	+	1.22474i		−	4.46151i	−1.06684	+	1.96516i	−4.40279			−3.72376	+	3.72376i	4.42439	+	4.42439i			3.00000i	−1.61466	−	5.44981i
158.5	−1.38958	+	1.38958i	−1.22474	−	1.22474i		−	1.86184i	2.21692	+	0.291998i	3.40375			−3.65447	+	3.65447i	−0.191982	−	0.191982i			3.00000i	−3.48633	+	2.67483i
158.6	−1.38958	+	1.38958i	1.22474	+	1.22474i		−	1.86184i	−0.291998	−	2.21692i	−3.40375			−0.803024	+	0.803024i	−0.191982	−	0.191982i			3.00000i	3.48633	+	2.67483i
158.7	−0.938625	+	0.938625i	−1.22474	−	1.22474i			0.237965i	−1.53930	−	1.62189i	2.29915			3.22746	−	3.22746i	−2.10061	−	2.10061i			3.00000i	2.96718	+	0.0775213i
158.8	−0.938625	+	0.938625i	1.22474	+	1.22474i			0.237965i	1.62189	+	1.53930i	−2.29915			−1.89301	+	1.89301i	−2.10061	−	2.10061i			3.00000i	−2.96718	+	0.0775213i
158.9	−0.278703	+	0.278703i	−1.22474	−	1.22474i			1.84465i	−2.01818	+	0.962772i	0.682680			−1.49838	+	1.49838i	−1.07151	−	1.07151i			3.00000i	0.294146	−	0.830801i
158.10	−0.278703	+	0.278703i	1.22474	+	1.22474i			1.84465i	−0.962772	+	2.01818i	−0.682680			3.42853	−	3.42853i	−1.07151	−	1.07151i			3.00000i	−0.294146	−	0.830801i
158.11	0.278703	−	0.278703i	−1.22474	−	1.22474i			1.84465i	0.962772	−	2.01818i	−0.682680			3.42853	−	3.42853i	1.07151	+	1.07151i			3.00000i	−0.294146	−	0.830801i
158.12	0.278703	−	0.278703i	1.22474	+	1.22474i			1.84465i	2.01818	−	0.962772i	0.682680			−1.49838	+	1.49838i	1.07151	+	1.07151i			3.00000i	0.294146	−	0.830801i
158.13	0.938625	−	0.938625i	−1.22474	−	1.22474i			0.237965i	−1.62189	−	1.53930i	−2.29915			−1.89301	+	1.89301i	2.10061	+	2.10061i			3.00000i	−2.96718	+	0.0775213i
158.14	0.938625	−	0.938625i	1.22474	+	1.22474i			0.237965i	1.53930	+	1.62189i	2.29915			3.22746	−	3.22746i	2.10061	+	2.10061i			3.00000i	2.96718	+	0.0775213i
158.15	1.38958	−	1.38958i	−1.22474	−	1.22474i		−	1.86184i	0.291998	+	2.21692i	−3.40375			−0.803024	+	0.803024i	0.191982	+	0.191982i			3.00000i	3.48633	+	2.67483i
158.16	1.38958	−	1.38958i	1.22474	+	1.22474i		−	1.86184i	−2.21692	−	0.291998i	3.40375			−3.65447	+	3.65447i	0.191982	+	0.191982i			3.00000i	−3.48633	+	2.67483i
158.17	1.79743	−	1.79743i	−1.22474	−	1.22474i		−	4.46151i	1.06684	−	1.96516i	−4.40279			−3.72376	+	3.72376i	−4.42439	−	4.42439i			3.00000i	−1.61466	−	5.44981i
158.18	1.79743	−	1.79743i	1.22474	+	1.22474i		−	4.46151i	1.96516	−	1.06684i	4.40279			−0.365573	+	0.365573i	−4.42439	−	4.42439i			3.00000i	1.61466	−	5.44981i
158.19	1.96968	−	1.96968i	−1.22474	−	1.22474i		−	5.75926i	0.407360	+	2.19865i	−4.82471			2.48452	−	2.48452i	−7.40454	−	7.40454i			3.00000i	5.13300	+	3.52826i
158.20	1.96968	−	1.96968i	1.22474	+	1.22474i		−	5.75926i	−2.19865	−	0.407360i	4.82471			2.79770	−	2.79770i	−7.40454	−	7.40454i			3.00000i	−5.13300	+	3.52826i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
159.d	odd	2	1	CM by \(\Q(\sqrt{-159}) \)
3.b	odd	2	1	inner
5.c	odd	4	1	inner
15.e	even	4	1	inner
53.b	even	2	1	inner
265.i	odd	4	1	inner
795.m	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	795.2.m.a	✓	40
3.b	odd	2	1	inner	795.2.m.a	✓	40
5.c	odd	4	1	inner	795.2.m.a	✓	40
15.e	even	4	1	inner	795.2.m.a	✓	40
53.b	even	2	1	inner	795.2.m.a	✓	40
159.d	odd	2	1	CM	795.2.m.a	✓	40
265.i	odd	4	1	inner	795.2.m.a	✓	40
795.m	even	4	1	inner	795.2.m.a	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
795.2.m.a	✓	40	1.a	even	1	1	trivial
795.2.m.a	✓	40	3.b	odd	2	1	inner
795.2.m.a	✓	40	5.c	odd	4	1	inner
795.2.m.a	✓	40	15.e	even	4	1	inner
795.2.m.a	✓	40	53.b	even	2	1	inner
795.2.m.a	✓	40	159.d	odd	2	1	CM
795.2.m.a	✓	40	265.i	odd	4	1	inner
795.2.m.a	✓	40	795.m	even	4	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{20} + 120T_{2}^{16} + 4400T_{2}^{12} + 50120T_{2}^{8} + 117600T_{2}^{4} + 2809 \) acting on \(S_{2}^{\mathrm{new}}(795, [\chi])\).