Properties

 Label 105.3.l.a Level 105 Weight 3 Character orbit 105.l Analytic conductor 2.861 Analytic rank 0 Dimension 24 CM no Inner twists 2

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 105.l (of order $$4$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$2.86104277578$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} - 40q^{10} - 48q^{12} + 64q^{13} - 184q^{16} + 24q^{17} + 24q^{18} + 72q^{20} + 8q^{22} + 8q^{23} - 136q^{25} - 80q^{26} + 96q^{30} + 96q^{31} + 56q^{32} - 72q^{33} + 168q^{36} + 8q^{37} + 56q^{38} + 232q^{40} + 320q^{41} - 112q^{43} - 72q^{45} + 320q^{46} + 64q^{47} + 192q^{48} - 256q^{50} - 192q^{51} + 96q^{52} - 72q^{53} - 80q^{55} - 336q^{56} + 48q^{57} - 512q^{58} - 192q^{60} - 496q^{61} - 776q^{62} + 312q^{65} - 192q^{66} - 192q^{67} + 568q^{68} + 112q^{70} - 144q^{71} + 144q^{72} + 224q^{73} + 144q^{75} + 416q^{76} + 112q^{77} - 216q^{78} - 528q^{80} - 216q^{81} + 352q^{82} - 32q^{83} + 24q^{85} + 240q^{86} + 384q^{87} + 216q^{88} - 24q^{90} + 1304q^{92} + 376q^{95} + 168q^{96} - 816q^{97} - 56q^{98} + O(q^{100})$$

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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
22.1 −2.72310 2.72310i −1.22474 + 1.22474i 10.8306i 4.39513 2.38387i 6.67022 −1.87083 1.87083i 18.6004 18.6004i 3.00000i −18.4599 5.47689i
22.2 −1.59930 1.59930i −1.22474 + 1.22474i 1.11554i −1.35929 4.81169i 3.91747 1.87083 + 1.87083i −4.61313 + 4.61313i 3.00000i −5.52142 + 9.86926i
22.3 −1.36784 1.36784i −1.22474 + 1.22474i 0.258033i 3.39663 + 3.66919i 3.35051 1.87083 + 1.87083i −5.82430 + 5.82430i 3.00000i 0.372817 9.66489i
22.4 −1.01289 1.01289i 1.22474 1.22474i 1.94811i 3.97454 3.03365i −2.48106 1.87083 + 1.87083i −6.02478 + 6.02478i 3.00000i −7.09851 0.953024i
22.5 −0.867675 0.867675i 1.22474 1.22474i 2.49428i −4.93004 0.833478i −2.12536 −1.87083 1.87083i −5.63493 + 5.63493i 3.00000i 3.55449 + 5.00086i
22.6 0.408558 + 0.408558i −1.22474 + 1.22474i 3.66616i 0.563288 4.96817i −1.00076 −1.87083 1.87083i 3.13207 3.13207i 3.00000i 2.25992 1.79965i
22.7 0.675544 + 0.675544i 1.22474 1.22474i 3.08728i 3.39488 + 3.67080i 1.65474 −1.87083 1.87083i 4.78777 4.78777i 3.00000i −0.186396 + 4.77318i
22.8 0.992944 + 0.992944i 1.22474 1.22474i 2.02813i −2.01954 4.57400i 2.43221 1.87083 + 1.87083i 5.98559 5.98559i 3.00000i 2.53644 6.54701i
22.9 2.08980 + 2.08980i −1.22474 + 1.22474i 4.73454i 0.137153 + 4.99812i −5.11895 −1.87083 1.87083i −1.53505 + 1.53505i 3.00000i −10.1585 + 10.7317i
22.10 2.24469 + 2.24469i 1.22474 1.22474i 6.07726i −3.05058 + 3.96156i 5.49834 1.87083 + 1.87083i −4.66280 + 4.66280i 3.00000i −15.7401 + 2.04487i
22.11 2.41688 + 2.41688i 1.22474 1.22474i 7.68258i 4.18124 2.74175i 5.92011 −1.87083 1.87083i −8.90034 + 8.90034i 3.00000i 16.7320 + 3.47908i
22.12 2.74240 + 2.74240i −1.22474 + 1.22474i 11.0415i −0.683416 4.95307i −6.71747 1.87083 + 1.87083i −19.3105 + 19.3105i 3.00000i 11.7091 15.4575i
43.1 −2.72310 + 2.72310i −1.22474 1.22474i 10.8306i 4.39513 + 2.38387i 6.67022 −1.87083 + 1.87083i 18.6004 + 18.6004i 3.00000i −18.4599 + 5.47689i
43.2 −1.59930 + 1.59930i −1.22474 1.22474i 1.11554i −1.35929 + 4.81169i 3.91747 1.87083 1.87083i −4.61313 4.61313i 3.00000i −5.52142 9.86926i
43.3 −1.36784 + 1.36784i −1.22474 1.22474i 0.258033i 3.39663 3.66919i 3.35051 1.87083 1.87083i −5.82430 5.82430i 3.00000i 0.372817 + 9.66489i
43.4 −1.01289 + 1.01289i 1.22474 + 1.22474i 1.94811i 3.97454 + 3.03365i −2.48106 1.87083 1.87083i −6.02478 6.02478i 3.00000i −7.09851 + 0.953024i
43.5 −0.867675 + 0.867675i 1.22474 + 1.22474i 2.49428i −4.93004 + 0.833478i −2.12536 −1.87083 + 1.87083i −5.63493 5.63493i 3.00000i 3.55449 5.00086i
43.6 0.408558 0.408558i −1.22474 1.22474i 3.66616i 0.563288 + 4.96817i −1.00076 −1.87083 + 1.87083i 3.13207 + 3.13207i 3.00000i 2.25992 + 1.79965i
43.7 0.675544 0.675544i 1.22474 + 1.22474i 3.08728i 3.39488 3.67080i 1.65474 −1.87083 + 1.87083i 4.78777 + 4.78777i 3.00000i −0.186396 4.77318i
43.8 0.992944 0.992944i 1.22474 + 1.22474i 2.02813i −2.01954 + 4.57400i 2.43221 1.87083 1.87083i 5.98559 + 5.98559i 3.00000i 2.53644 + 6.54701i
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 43.12 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.3.l.a 24
3.b odd 2 1 315.3.o.b 24
5.b even 2 1 525.3.l.e 24
5.c odd 4 1 inner 105.3.l.a 24
5.c odd 4 1 525.3.l.e 24
15.e even 4 1 315.3.o.b 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.3.l.a 24 1.a even 1 1 trivial
105.3.l.a 24 5.c odd 4 1 inner
315.3.o.b 24 3.b odd 2 1
315.3.o.b 24 15.e even 4 1
525.3.l.e 24 5.b even 2 1
525.3.l.e 24 5.c odd 4 1

Hecke kernels

This newform subspace is the entire newspace $$S_{3}^{\mathrm{new}}(105, [\chi])$$.

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database