Properties

Label 105.3.o.b
Level 105
Weight 3
Character orbit 105.o
Analytic conductor 2.861
Analytic rank 0
Dimension 40
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + 62q^{10} + 84q^{15} - 116q^{16} - 56q^{19} + 36q^{21} - 12q^{24} - 6q^{25} - 20q^{30} - 444q^{31} + 256q^{34} - 688q^{36} + 168q^{39} + 54q^{40} - 40q^{45} + 304q^{46} + 156q^{49} + 156q^{51} - 140q^{54} - 500q^{55} - 130q^{60} + 288q^{61} + 472q^{64} + 340q^{66} - 272q^{69} + 710q^{70} - 524q^{75} + 400q^{76} - 340q^{79} + 496q^{84} + 896q^{85} + 1356q^{90} - 656q^{91} - 560q^{94} + 472q^{96} - 336q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
44.1 −1.85988 + 3.22141i −2.47330 + 1.69788i −4.91833 8.51879i 4.36624 2.43637i −0.869509 11.1254i −4.87678 5.02166i 21.7110 3.23443 8.39872i −0.272141 + 18.5968i
44.2 −1.85988 + 3.22141i 2.70705 1.29300i −4.91833 8.51879i −0.0731607 4.99946i −0.869509 + 11.1254i 4.87678 + 5.02166i 21.7110 5.65629 7.00046i 16.2414 + 9.06274i
44.3 −1.60486 + 2.77971i −2.69226 1.32352i −3.15118 5.45800i −4.78223 + 1.45954i 7.99972 5.35963i 6.02754 3.55932i 7.38994 5.49658 + 7.12655i 3.61773 15.6356i
44.4 −1.60486 + 2.77971i 0.199928 2.99333i −3.15118 5.45800i 1.12712 + 4.87130i 7.99972 + 5.35963i −6.02754 + 3.55932i 7.38994 −8.92006 1.19690i −15.3497 4.68473i
44.5 −0.949639 + 1.64482i −2.65035 1.40558i 0.196373 + 0.340128i 4.51617 2.14574i 4.82880 3.02455i 4.60961 + 5.26797i −8.34304 5.04868 + 7.45056i −0.759373 + 9.46598i
44.6 −0.949639 + 1.64482i 0.107903 2.99806i 0.196373 + 0.340128i −0.399822 4.98399i 4.82880 + 3.02455i −4.60961 5.26797i −8.34304 −8.97671 0.647002i 8.57746 + 4.07535i
44.7 −0.897800 + 1.55504i −2.08367 + 2.15832i 0.387909 + 0.671879i −3.31295 3.74491i −1.48554 5.17791i −1.39571 + 6.85945i −8.57546 −0.316668 8.99443i 8.79784 1.78957i
44.8 −0.897800 + 1.55504i 2.91099 0.725349i 0.387909 + 0.671879i 4.89966 + 0.996641i −1.48554 + 5.17791i 1.39571 6.85945i −8.57546 7.94774 4.22297i −5.94873 + 6.72437i
44.9 −0.0859580 + 0.148884i 0.346935 + 2.97987i 1.98522 + 3.43851i 4.85467 1.19675i −0.473476 0.204491i −6.99566 + 0.246384i −1.37025 −8.75927 + 2.06764i −0.239121 + 0.825650i
44.10 −0.0859580 + 0.148884i 2.40718 + 1.79039i 1.98522 + 3.43851i −1.39092 4.80264i −0.473476 + 0.204491i 6.99566 0.246384i −1.37025 2.58900 + 8.61957i 0.834595 + 0.205740i
44.11 0.0859580 0.148884i −2.40718 1.79039i 1.98522 + 3.43851i −4.85467 + 1.19675i −0.473476 + 0.204491i −6.99566 + 0.246384i 1.37025 2.58900 + 8.61957i −0.239121 + 0.825650i
44.12 0.0859580 0.148884i −0.346935 2.97987i 1.98522 + 3.43851i 1.39092 + 4.80264i −0.473476 0.204491i 6.99566 0.246384i 1.37025 −8.75927 + 2.06764i 0.834595 + 0.205740i
44.13 0.897800 1.55504i −2.91099 + 0.725349i 0.387909 + 0.671879i 3.31295 + 3.74491i −1.48554 + 5.17791i −1.39571 + 6.85945i 8.57546 7.94774 4.22297i 8.79784 1.78957i
44.14 0.897800 1.55504i 2.08367 2.15832i 0.387909 + 0.671879i −4.89966 0.996641i −1.48554 5.17791i 1.39571 6.85945i 8.57546 −0.316668 8.99443i −5.94873 + 6.72437i
44.15 0.949639 1.64482i −0.107903 + 2.99806i 0.196373 + 0.340128i −4.51617 + 2.14574i 4.82880 + 3.02455i 4.60961 + 5.26797i 8.34304 −8.97671 0.647002i −0.759373 + 9.46598i
44.16 0.949639 1.64482i 2.65035 + 1.40558i 0.196373 + 0.340128i 0.399822 + 4.98399i 4.82880 3.02455i −4.60961 5.26797i 8.34304 5.04868 + 7.45056i 8.57746 + 4.07535i
44.17 1.60486 2.77971i −0.199928 + 2.99333i −3.15118 5.45800i 4.78223 1.45954i 7.99972 + 5.35963i 6.02754 3.55932i −7.38994 −8.92006 1.19690i 3.61773 15.6356i
44.18 1.60486 2.77971i 2.69226 + 1.32352i −3.15118 5.45800i −1.12712 4.87130i 7.99972 5.35963i −6.02754 + 3.55932i −7.38994 5.49658 + 7.12655i −15.3497 4.68473i
44.19 1.85988 3.22141i −2.70705 + 1.29300i −4.91833 8.51879i −4.36624 + 2.43637i −0.869509 + 11.1254i −4.87678 5.02166i −21.7110 5.65629 7.00046i −0.272141 + 18.5968i
44.20 1.85988 3.22141i 2.47330 1.69788i −4.91833 8.51879i 0.0731607 + 4.99946i −0.869509 11.1254i 4.87678 + 5.02166i −21.7110 3.23443 8.39872i 16.2414 + 9.06274i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 74.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
7.c even 3 1 inner
15.d odd 2 1 inner
21.h odd 6 1 inner
35.j even 6 1 inner
105.o odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.3.o.b 40
3.b odd 2 1 inner 105.3.o.b 40
5.b even 2 1 inner 105.3.o.b 40
7.c even 3 1 inner 105.3.o.b 40
15.d odd 2 1 inner 105.3.o.b 40
21.h odd 6 1 inner 105.3.o.b 40
35.j even 6 1 inner 105.3.o.b 40
105.o odd 6 1 inner 105.3.o.b 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.3.o.b 40 1.a even 1 1 trivial
105.3.o.b 40 3.b odd 2 1 inner
105.3.o.b 40 5.b even 2 1 inner
105.3.o.b 40 7.c even 3 1 inner
105.3.o.b 40 15.d odd 2 1 inner
105.3.o.b 40 21.h odd 6 1 inner
105.3.o.b 40 35.j even 6 1 inner
105.3.o.b 40 105.o odd 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{20} + \cdots\) acting on \(S_{3}^{\mathrm{new}}(105, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database