Properties

Label 105.3.f.a
Level 105
Weight 3
Character orbit 105.f
Analytic conductor 2.861
Analytic rank 0
Dimension 24
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.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24q + 52q^{4} - 22q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q + 52q^{4} - 22q^{9} - 24q^{10} + 26q^{15} + 4q^{16} + 72q^{19} + 14q^{21} - 156q^{24} - 64q^{25} - 32q^{30} - 40q^{31} - 144q^{34} + 36q^{36} + 62q^{39} - 40q^{40} + 120q^{45} - 104q^{46} - 168q^{49} + 70q^{51} + 60q^{54} - 16q^{55} - 348q^{60} + 432q^{61} - 364q^{64} + 284q^{66} + 404q^{69} + 140q^{70} + 204q^{75} + 152q^{76} + 108q^{79} - 158q^{81} + 112q^{84} + 196q^{85} - 152q^{90} - 84q^{91} + 808q^{94} - 516q^{96} + 582q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
29.1 −3.57140 2.50375 1.65264i 8.75491 −0.280149 + 4.99215i −8.94190 + 5.90225i 2.64575i −16.9817 3.53755 8.27561i 1.00052 17.8290i
29.2 −3.57140 2.50375 + 1.65264i 8.75491 −0.280149 4.99215i −8.94190 5.90225i 2.64575i −16.9817 3.53755 + 8.27561i 1.00052 + 17.8290i
29.3 −3.21327 −1.93400 2.29339i 6.32511 4.77035 1.49792i 6.21446 + 7.36929i 2.64575i −7.47120 −1.51929 + 8.87084i −15.3284 + 4.81322i
29.4 −3.21327 −1.93400 + 2.29339i 6.32511 4.77035 + 1.49792i 6.21446 7.36929i 2.64575i −7.47120 −1.51929 8.87084i −15.3284 4.81322i
29.5 −2.80814 0.0756962 2.99904i 3.88565 −4.04610 2.93753i −0.212566 + 8.42174i 2.64575i 0.321110 −8.98854 0.454033i 11.3620 + 8.24901i
29.6 −2.80814 0.0756962 + 2.99904i 3.88565 −4.04610 + 2.93753i −0.212566 8.42174i 2.64575i 0.321110 −8.98854 + 0.454033i 11.3620 8.24901i
29.7 −1.87229 −2.98471 0.302541i −0.494516 −2.18081 + 4.49934i 5.58825 + 0.566446i 2.64575i 8.41505 8.81694 + 1.80599i 4.08312 8.42408i
29.8 −1.87229 −2.98471 + 0.302541i −0.494516 −2.18081 4.49934i 5.58825 0.566446i 2.64575i 8.41505 8.81694 1.80599i 4.08312 + 8.42408i
29.9 −1.50770 2.08699 2.15510i −1.72685 4.79474 + 1.41790i −3.14656 + 3.24924i 2.64575i 8.63435 −0.288904 8.99536i −7.22902 2.13777i
29.10 −1.50770 2.08699 + 2.15510i −1.72685 4.79474 1.41790i −3.14656 3.24924i 2.64575i 8.63435 −0.288904 + 8.99536i −7.22902 + 2.13777i
29.11 −0.505667 −0.985457 2.83353i −3.74430 −0.221081 + 4.99511i 0.498313 + 1.43282i 2.64575i 3.91604 −7.05775 + 5.58464i 0.111793 2.52586i
29.12 −0.505667 −0.985457 + 2.83353i −3.74430 −0.221081 4.99511i 0.498313 1.43282i 2.64575i 3.91604 −7.05775 5.58464i 0.111793 + 2.52586i
29.13 0.505667 0.985457 2.83353i −3.74430 0.221081 4.99511i 0.498313 1.43282i 2.64575i −3.91604 −7.05775 5.58464i 0.111793 2.52586i
29.14 0.505667 0.985457 + 2.83353i −3.74430 0.221081 + 4.99511i 0.498313 + 1.43282i 2.64575i −3.91604 −7.05775 + 5.58464i 0.111793 + 2.52586i
29.15 1.50770 −2.08699 2.15510i −1.72685 −4.79474 1.41790i −3.14656 3.24924i 2.64575i −8.63435 −0.288904 + 8.99536i −7.22902 2.13777i
29.16 1.50770 −2.08699 + 2.15510i −1.72685 −4.79474 + 1.41790i −3.14656 + 3.24924i 2.64575i −8.63435 −0.288904 8.99536i −7.22902 + 2.13777i
29.17 1.87229 2.98471 0.302541i −0.494516 2.18081 4.49934i 5.58825 0.566446i 2.64575i −8.41505 8.81694 1.80599i 4.08312 8.42408i
29.18 1.87229 2.98471 + 0.302541i −0.494516 2.18081 + 4.49934i 5.58825 + 0.566446i 2.64575i −8.41505 8.81694 + 1.80599i 4.08312 + 8.42408i
29.19 2.80814 −0.0756962 2.99904i 3.88565 4.04610 + 2.93753i −0.212566 8.42174i 2.64575i −0.321110 −8.98854 + 0.454033i 11.3620 + 8.24901i
29.20 2.80814 −0.0756962 + 2.99904i 3.88565 4.04610 2.93753i −0.212566 + 8.42174i 2.64575i −0.321110 −8.98854 0.454033i 11.3620 8.24901i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 29.24
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
15.d odd 2 1 inner

Twists

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

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