Newform orbit 1805.2.b.l

• Label: 1805.2.b.l
• Level: $1805$
• Weight: $2$
• Character orbit: 1805.b
• Analytic conductor: $14.413$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$1805 = 5 \cdot 19^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1805.b (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

$\operatorname{Tr}(f)(q) =$ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 + 6 * q^10 + 12 * q^11 + 24 * q^14 + 9 * q^15 + 6 * q^16 + 21 * q^20 - 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 + 36 * q^29 - 18 * q^30 - 42 * q^31 + 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 - 12 * q^40 - 60 * q^41 + 30 * q^44 + 9 * q^45 - 6 * q^46 - 12 * q^49 - 18 * q^50 - 30 * q^51 + 24 * q^54 + 33 * q^55 - 18 * q^56 + 60 * q^59 + 42 * q^60 + 30 * q^61 - 18 * q^65 + 36 * q^66 + 66 * q^69 - 9 * q^70 - 96 * q^71 - 24 * q^74 - 36 * q^75 + 72 * q^79 - 42 * q^80 - 96 * q^81 - 54 * q^84 - 27 * q^85 - 108 * q^86 + 84 * q^89 + 93 * q^90 - 96 * q^91 + 36 * q^94 - 120 * q^96

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
1084.1		−	2.68669i		−	2.14658i	−5.21828			−1.71227	+	1.43810i	−5.76720					2.78303i			8.64651i	−1.60782			3.86371	+	4.60034i
1084.2		−	2.37097i		−	2.28512i	−3.62149			1.17411	−	1.90301i	−5.41794				−	1.63677i			3.84450i	−2.22176			−4.51198	−	2.78378i
1084.3		−	2.32462i			1.14858i	−3.40387			−2.01201	+	0.975617i	2.67001				−	0.143302i			3.26348i	1.68077			2.26794	+	4.67716i
1084.4		−	1.96177i			0.187708i	−1.84854			1.81111	+	1.31144i	0.368240					0.677067i		−	0.297123i	2.96477			2.57274	−	3.55299i
1084.5		−	1.78468i			2.38377i	−1.18508			−1.16534	−	1.90840i	4.25426					4.23911i		−	1.45438i	−2.68235			−3.40588	+	2.07976i
1084.6		−	1.61907i			1.18857i	−0.621387			0.326390	+	2.21212i	1.92438				−	2.23190i		−	2.23207i	1.58730			3.58157	−	0.528448i
1084.7		−	1.47917i		−	2.48321i	−0.187941			0.111989	−	2.23326i	−3.67308					3.24988i		−	2.68034i	−3.16631			−3.30337	−	0.165651i
1084.8		−	1.22159i			0.804421i	0.507728			−2.23387	+	0.0991400i	0.982669				−	3.79180i		−	3.06341i	2.35291			0.121108	+	2.72886i
1084.9		−	1.04740i		−	0.531453i	0.902948			1.65192	+	1.50704i	−0.556645					2.74033i		−	3.04056i	2.71756			1.57847	−	1.73023i
1084.10		−	0.449373i		−	1.95684i	1.79806			1.87757	+	1.21438i	−0.879352					2.06079i		−	1.70675i	−0.829224			0.545709	−	0.843732i
1084.11		−	0.249751i		−	2.30156i	1.93762			−2.08007	+	0.820550i	−0.574816				−	3.96043i		−	0.983424i	−2.29718			0.204933	+	0.519499i
1084.12		−	0.244477i			2.73837i	1.94023			0.750459	−	2.10637i	0.669469					1.94027i		−	0.963297i	−4.49866			−0.514961	−	0.183470i
1084.13			0.244477i		−	2.73837i	1.94023			0.750459	+	2.10637i	0.669469				−	1.94027i			0.963297i	−4.49866			−0.514961	+	0.183470i
1084.14			0.249751i			2.30156i	1.93762			−2.08007	−	0.820550i	−0.574816					3.96043i			0.983424i	−2.29718			0.204933	−	0.519499i
1084.15			0.449373i			1.95684i	1.79806			1.87757	−	1.21438i	−0.879352				−	2.06079i			1.70675i	−0.829224			0.545709	+	0.843732i
1084.16			1.04740i			0.531453i	0.902948			1.65192	−	1.50704i	−0.556645				−	2.74033i			3.04056i	2.71756			1.57847	+	1.73023i
1084.17			1.22159i		−	0.804421i	0.507728			−2.23387	−	0.0991400i	0.982669					3.79180i			3.06341i	2.35291			0.121108	−	2.72886i
1084.18			1.47917i			2.48321i	−0.187941			0.111989	+	2.23326i	−3.67308				−	3.24988i			2.68034i	−3.16631			−3.30337	+	0.165651i
1084.19			1.61907i		−	1.18857i	−0.621387			0.326390	−	2.21212i	1.92438					2.23190i			2.23207i	1.58730			3.58157	+	0.528448i
1084.20			1.78468i		−	2.38377i	−1.18508			−1.16534	+	1.90840i	4.25426				−	4.23911i			1.45438i	−2.68235			−3.40588	−	2.07976i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1805.2.b.l		24
5.b	even	2	1	inner	1805.2.b.l		24
5.c	odd	4	2		9025.2.a.ct		24
19.b	odd	2	1		1805.2.b.k		24
19.f	odd	18	2		95.2.p.a	✓	48
57.j	even	18	2		855.2.da.b		48
95.d	odd	2	1		1805.2.b.k		24
95.g	even	4	2		9025.2.a.cu		24
95.o	odd	18	2		95.2.p.a	✓	48
95.r	even	36	4		475.2.l.f		48
285.bf	even	18	2		855.2.da.b		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.2.p.a	✓	48	19.f	odd	18	2
95.2.p.a	✓	48	95.o	odd	18	2
475.2.l.f		48	95.r	even	36	4
855.2.da.b		48	57.j	even	18	2
855.2.da.b		48	285.bf	even	18	2
1805.2.b.k		24	19.b	odd	2	1
1805.2.b.k		24	95.d	odd	2	1
1805.2.b.l		24	1.a	even	1	1	trivial
1805.2.b.l		24	5.b	even	2	1	inner
9025.2.a.ct		24	5.c	odd	4	2
9025.2.a.cu		24	95.g	even	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(1805, [\chi])$:

T2^24 + 33*T2^22 + 468*T2^20 + 3743*T2^18 + 18618*T2^16 + 59871*T2^14 + 125215*T2^12 + 166671*T2^10 + 133557*T2^8 + 57610*T2^6 + 10782*T2^4 + 783*T2^2 + 19

T29^12 - 18*T29^11 + 45*T29^10 + 756*T29^9 - 3600*T29^8 - 9369*T29^7 + 65511*T29^6 + 13797*T29^5 - 425574*T29^4 + 286713*T29^3 + 757431*T29^2 - 567891*T29 - 263169