Newform orbit 595.2.l.a

• Label: 595.2.l.a
• Level: $595$
• Weight: $2$
• Character orbit: 595.l
• Analytic conductor: $4.751$
• Analytic rank: $0$
• Dimension: $136$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 595 = 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	595.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.75109892027\)
Analytic rank:	\(0\)
Dimension:	\(136\)
Relative dimension:	\(68\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 136 q - 8 q^{7} - 112 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
132.1	−1.94062	+	1.94062i		−	1.52536i		−	5.53200i	1.98818	−	1.02330i	2.96014	+	2.96014i	−1.98842	−	1.74534i	6.85427	+	6.85427i	0.673281			−1.87247	+	5.84413i
132.2	−1.94062	+	1.94062i			1.52536i		−	5.53200i	−1.98818	+	1.02330i	−2.96014	−	2.96014i	−1.98842	+	1.74534i	6.85427	+	6.85427i	0.673281			1.87247	−	5.84413i
132.3	−1.93050	+	1.93050i		−	2.47104i		−	5.45366i	0.442117	+	2.19192i	4.77035	+	4.77035i	1.83132	+	1.90952i	6.66729	+	6.66729i	−3.10605			−5.08502	−	3.37800i
132.4	−1.93050	+	1.93050i			2.47104i		−	5.45366i	−0.442117	−	2.19192i	−4.77035	−	4.77035i	1.83132	−	1.90952i	6.66729	+	6.66729i	−3.10605			5.08502	+	3.37800i
132.5	−1.66183	+	1.66183i		−	0.607313i		−	3.52335i	0.871230	−	2.05936i	1.00925	+	1.00925i	0.832713	+	2.51129i	2.53154	+	2.53154i	2.63117			1.97447	+	4.87014i
132.6	−1.66183	+	1.66183i			0.607313i		−	3.52335i	−0.871230	+	2.05936i	−1.00925	−	1.00925i	0.832713	−	2.51129i	2.53154	+	2.53154i	2.63117			−1.97447	−	4.87014i
132.7	−1.65833	+	1.65833i		−	2.19900i		−	3.50014i	−2.22131	−	0.256488i	3.64667	+	3.64667i	1.98144	−	1.75325i	2.48773	+	2.48773i	−1.83560			4.10901	−	3.25833i
132.8	−1.65833	+	1.65833i			2.19900i		−	3.50014i	2.22131	+	0.256488i	−3.64667	−	3.64667i	1.98144	+	1.75325i	2.48773	+	2.48773i	−1.83560			−4.10901	+	3.25833i
132.9	−1.58596	+	1.58596i		−	0.599910i		−	3.03053i	−1.23203	−	1.86604i	0.951432	+	0.951432i	−2.36357	−	1.18893i	1.63438	+	1.63438i	2.64011			4.91341	+	1.00551i
132.10	−1.58596	+	1.58596i			0.599910i		−	3.03053i	1.23203	+	1.86604i	−0.951432	−	0.951432i	−2.36357	+	1.18893i	1.63438	+	1.63438i	2.64011			−4.91341	−	1.00551i
132.11	−1.33560	+	1.33560i		−	2.46300i		−	1.56768i	−1.35457	+	1.77909i	3.28960	+	3.28960i	−2.61348	+	0.412000i	−0.577414	−	0.577414i	−3.06639			−0.566989	−	4.18532i
132.12	−1.33560	+	1.33560i			2.46300i		−	1.56768i	1.35457	−	1.77909i	−3.28960	−	3.28960i	−2.61348	−	0.412000i	−0.577414	−	0.577414i	−3.06639			0.566989	+	4.18532i
132.13	−1.31827	+	1.31827i		−	3.15324i		−	1.47569i	2.21764	+	0.286471i	4.15683	+	4.15683i	−1.03865	−	2.43335i	−0.691187	−	0.691187i	−6.94294			−3.30110	+	2.54581i
132.14	−1.31827	+	1.31827i			3.15324i		−	1.47569i	−2.21764	−	0.286471i	−4.15683	−	4.15683i	−1.03865	+	2.43335i	−0.691187	−	0.691187i	−6.94294			3.30110	−	2.54581i
132.15	−1.24826	+	1.24826i		−	1.98186i		−	1.11632i	0.950841	−	2.02383i	2.47389	+	2.47389i	2.41359	−	1.08378i	−1.10307	−	1.10307i	−0.927784			1.33938	+	3.71317i
132.16	−1.24826	+	1.24826i			1.98186i		−	1.11632i	−0.950841	+	2.02383i	−2.47389	−	2.47389i	2.41359	+	1.08378i	−1.10307	−	1.10307i	−0.927784			−1.33938	−	3.71317i
132.17	−1.11093	+	1.11093i		−	1.72727i		−	0.468329i	1.35899	+	1.77571i	1.91887	+	1.91887i	2.61846	+	0.379028i	−1.70158	−	1.70158i	0.0165551			−3.48243	−	0.462939i
132.18	−1.11093	+	1.11093i			1.72727i		−	0.468329i	−1.35899	−	1.77571i	−1.91887	−	1.91887i	2.61846	−	0.379028i	−1.70158	−	1.70158i	0.0165551			3.48243	+	0.462939i
132.19	−1.01141	+	1.01141i		−	0.227273i		−	0.0459147i	1.38344	+	1.75673i	0.229867	+	0.229867i	−1.73940	−	1.99361i	−1.97639	−	1.97639i	2.94835			−3.17601	−	0.377554i
132.20	−1.01141	+	1.01141i			0.227273i		−	0.0459147i	−1.38344	−	1.75673i	−0.229867	−	0.229867i	−1.73940	+	1.99361i	−1.97639	−	1.97639i	2.94835			3.17601	+	0.377554i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
85.i	odd	4	1	inner
595.l	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	595.2.l.a	✓	136
5.c	odd	4	1		595.2.r.a	yes	136
7.b	odd	2	1	inner	595.2.l.a	✓	136
17.c	even	4	1		595.2.r.a	yes	136
35.f	even	4	1		595.2.r.a	yes	136
85.i	odd	4	1	inner	595.2.l.a	✓	136
119.f	odd	4	1		595.2.r.a	yes	136
595.l	even	4	1	inner	595.2.l.a	✓	136

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
595.2.l.a	✓	136	1.a	even	1	1	trivial
595.2.l.a	✓	136	7.b	odd	2	1	inner
595.2.l.a	✓	136	85.i	odd	4	1	inner
595.2.l.a	✓	136	595.l	even	4	1	inner
595.2.r.a	yes	136	5.c	odd	4	1
595.2.r.a	yes	136	17.c	even	4	1
595.2.r.a	yes	136	35.f	even	4	1
595.2.r.a	yes	136	119.f	odd	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(595, [\chi])\).