Properties

Label 105.3.t.b
Level 105
Weight 3
Character orbit 105.t
Analytic conductor 2.861
Analytic rank 0
Dimension 36
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + 20q^{10} - 42q^{12} - 100q^{13} + 20q^{15} - 12q^{16} - 14q^{18} + 50q^{19} - 12q^{21} + 256q^{22} - 140q^{24} + 90q^{25} + 4q^{27} - 48q^{28} + 60q^{30} - 82q^{31} - 76q^{33} - 64q^{34} + 296q^{36} - 26q^{37} - 130q^{39} - 60q^{40} - 98q^{42} - 204q^{43} + 40q^{45} + 28q^{46} + 532q^{48} - 382q^{49} + 208q^{51} + 200q^{52} - 44q^{54} - 160q^{55} + 252q^{57} + 264q^{58} - 130q^{60} - 324q^{61} - 258q^{63} - 24q^{64} - 164q^{66} - 142q^{67} - 112q^{69} + 200q^{70} - 322q^{72} + 386q^{73} - 20q^{75} - 424q^{76} - 440q^{78} + 334q^{79} + 186q^{81} - 68q^{82} + 80q^{84} - 200q^{85} + 342q^{87} + 180q^{88} + 100q^{90} + 46q^{91} - 2q^{93} + 324q^{94} + 732q^{96} + 1616q^{97} + 384q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
11.1 −3.31814 + 1.91573i 1.84164 + 2.36819i 5.34002 9.24919i −1.93649 + 1.11803i −10.6476 4.32991i −5.86414 + 3.82255i 25.5943i −2.21669 + 8.72274i 4.28370 7.41958i
11.2 −2.61597 + 1.51033i −0.469377 2.96305i 2.56220 4.43785i 1.93649 1.11803i 5.70307 + 7.04234i −4.99419 + 4.90490i 3.39641i −8.55937 + 2.78158i −3.37720 + 5.84948i
11.3 −2.60397 + 1.50340i 2.88780 0.812762i 2.52044 4.36553i 1.93649 1.11803i −6.29785 + 6.45794i −0.494553 6.98251i 3.12973i 7.67884 4.69420i −3.36171 + 5.82265i
11.4 −2.46897 + 1.42546i −2.92531 0.665249i 2.06389 3.57476i −1.93649 + 1.11803i 8.17081 2.52744i −5.93505 3.71149i 0.364297i 8.11489 + 3.89212i 3.18743 5.52080i
11.5 −2.31825 + 1.33844i 2.46021 1.71679i 1.58287 2.74161i −1.93649 + 1.11803i −3.40557 + 7.27281i 4.89419 + 5.00469i 2.23323i 3.10528 8.44732i 2.99285 5.18377i
11.6 −1.50527 + 0.869067i −1.65926 + 2.49937i −0.489445 + 0.847743i −1.93649 + 1.11803i 0.325501 5.20423i 2.93407 + 6.35541i 8.65398i −3.49374 8.29420i 1.94329 3.36588i
11.7 −0.987174 + 0.569945i −0.202464 2.99316i −1.35032 + 2.33883i −1.93649 + 1.11803i 1.90581 + 2.83938i 2.61061 6.49498i 7.63801i −8.91802 + 1.21201i 1.27444 2.20739i
11.8 −0.860118 + 0.496589i 2.51213 + 1.63987i −1.50680 + 2.60985i 1.93649 1.11803i −2.97507 0.162987i −1.66850 + 6.79824i 6.96575i 3.62163 + 8.23916i −1.11041 + 1.92328i
11.9 −0.644768 + 0.372257i −2.67627 + 1.35556i −1.72285 + 2.98406i 1.93649 1.11803i 1.22096 1.87029i −5.98242 3.63464i 5.54343i 5.32489 7.25573i −0.832392 + 1.44175i
11.10 0.644768 0.372257i 0.164184 + 2.99550i −1.72285 + 2.98406i −1.93649 + 1.11803i 1.22096 + 1.87029i −5.98242 3.63464i 5.54343i −8.94609 + 0.983626i −0.832392 + 1.44175i
11.11 0.860118 0.496589i −2.67624 1.35563i −1.50680 + 2.60985i −1.93649 + 1.11803i −2.97507 + 0.162987i −1.66850 + 6.79824i 6.96575i 5.32451 + 7.25600i −1.11041 + 1.92328i
11.12 0.987174 0.569945i 2.69338 1.32124i −1.35032 + 2.33883i 1.93649 1.11803i 1.90581 2.83938i 2.61061 6.49498i 7.63801i 5.50864 7.11722i 1.27444 2.20739i
11.13 1.50527 0.869067i −1.33489 + 2.68664i −0.489445 + 0.847743i 1.93649 1.11803i 0.325501 + 5.20423i 2.93407 + 6.35541i 8.65398i −5.43612 7.17277i 1.94329 3.36588i
11.14 2.31825 1.33844i 0.256676 2.98900i 1.58287 2.74161i 1.93649 1.11803i −3.40557 7.27281i 4.89419 + 5.00469i 2.23323i −8.86824 1.53441i 2.99285 5.18377i
11.15 2.46897 1.42546i 2.03878 + 2.20077i 2.06389 3.57476i 1.93649 1.11803i 8.17081 + 2.52744i −5.93505 3.71149i 0.364297i −0.686770 + 8.97376i 3.18743 5.52080i
11.16 2.60397 1.50340i −0.740030 2.90729i 2.52044 4.36553i −1.93649 + 1.11803i −6.29785 6.45794i −0.494553 6.98251i 3.12973i −7.90471 + 4.30297i −3.36171 + 5.82265i
11.17 2.61597 1.51033i 2.80077 1.07503i 2.56220 4.43785i −1.93649 + 1.11803i 5.70307 7.04234i −4.99419 + 4.90490i 3.39641i 6.68860 6.02184i −3.37720 + 5.84948i
11.18 3.31814 1.91573i −2.97174 0.410813i 5.34002 9.24919i 1.93649 1.11803i −10.6476 + 4.32991i −5.86414 + 3.82255i 25.5943i 8.66247 + 2.44166i 4.28370 7.41958i
86.1 −3.31814 1.91573i 1.84164 2.36819i 5.34002 + 9.24919i −1.93649 1.11803i −10.6476 + 4.32991i −5.86414 3.82255i 25.5943i −2.21669 8.72274i 4.28370 + 7.41958i
86.2 −2.61597 1.51033i −0.469377 + 2.96305i 2.56220 + 4.43785i 1.93649 + 1.11803i 5.70307 7.04234i −4.99419 4.90490i 3.39641i −8.55937 2.78158i −3.37720 5.84948i
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 86.18
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
7.c even 3 1 inner
21.h 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.t.b 36
3.b odd 2 1 inner 105.3.t.b 36
7.c even 3 1 inner 105.3.t.b 36
21.h odd 6 1 inner 105.3.t.b 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.3.t.b 36 1.a even 1 1 trivial
105.3.t.b 36 3.b odd 2 1 inner
105.3.t.b 36 7.c even 3 1 inner
105.3.t.b 36 21.h odd 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{36} - \cdots\) acting on \(S_{3}^{\mathrm{new}}(105, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database