Properties

Label 105.3.w.a
Level 105
Weight 3
Character orbit 105.w
Analytic conductor 2.861
Analytic rank 0
Dimension 112
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.w (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(28\) over \(\Q(\zeta_{12})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 112q - 6q^{3} - 16q^{7} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 112q - 6q^{3} - 16q^{7} - 60q^{10} - 30q^{12} - 20q^{15} + 120q^{16} + 46q^{18} - 96q^{21} - 80q^{22} + 28q^{25} - 136q^{28} - 80q^{30} - 24q^{31} - 36q^{33} - 272q^{36} + 60q^{37} - 72q^{40} + 338q^{42} - 48q^{43} + 384q^{45} + 40q^{46} + 176q^{51} - 204q^{52} + 344q^{57} - 284q^{58} - 214q^{60} - 912q^{61} + 132q^{63} - 444q^{66} - 36q^{67} + 208q^{70} - 638q^{72} + 708q^{73} + 42q^{75} + 664q^{78} + 8q^{81} + 1104q^{82} + 264q^{85} + 246q^{87} + 180q^{88} + 632q^{91} + 196q^{93} + 2184q^{96} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 −3.72728 0.998723i 2.12159 + 2.12105i 9.43110 + 5.44505i 4.76718 + 1.50798i −5.78944 10.0246i −6.13877 + 3.36385i −18.8000 18.8000i 0.00230342 + 9.00000i −16.2626 10.3818i
17.2 −3.32412 0.890695i −2.80275 1.06987i 6.79233 + 3.92155i 3.30138 3.75512i 8.36374 + 6.05276i 3.32240 6.16130i −9.35192 9.35192i 6.71077 + 5.99713i −14.3188 + 9.54193i
17.3 −3.26791 0.875634i −2.44299 + 1.74120i 6.44841 + 3.72299i −4.71757 + 1.65668i 9.50814 3.55093i 1.33404 + 6.87171i −8.24376 8.24376i 2.93642 8.50749i 16.8672 1.28301i
17.4 −3.02468 0.810462i −0.664693 2.92544i 5.02776 + 2.90278i −2.83293 + 4.12001i −0.360468 + 9.38723i −5.96475 3.66357i −3.99791 3.99791i −8.11637 + 3.88904i 11.9078 10.1658i
17.5 −2.63032 0.704792i 1.27430 + 2.71591i 2.95775 + 1.70766i −2.97248 4.02050i −1.43765 8.04182i 6.12741 3.38450i 1.12583 + 1.12583i −5.75234 + 6.92175i 4.98495 + 12.6702i
17.6 −2.58075 0.691511i 1.70571 2.46791i 2.71800 + 1.56924i 4.71996 + 1.64985i −6.10859 + 5.18955i 6.61831 + 2.27990i 1.62763 + 1.62763i −3.18114 8.41905i −11.0402 7.52176i
17.7 −2.40293 0.643864i 2.79517 1.08950i 1.89543 + 1.09433i −1.28155 4.83297i −7.41810 + 0.818277i −6.92060 1.05130i 3.18629 + 3.18629i 6.62599 6.09067i −0.0322977 + 12.4385i
17.8 −1.98706 0.532431i −0.853896 + 2.87591i 0.200820 + 0.115943i 1.13457 + 4.86958i 3.22797 5.25996i −2.37777 6.58378i 5.48120 + 5.48120i −7.54172 4.91146i 0.338264 10.2802i
17.9 −1.55206 0.415874i −2.55828 + 1.56691i −1.22815 0.709073i 3.76090 3.29479i 4.62225 1.36802i −5.75785 + 3.98085i 6.15604 + 6.15604i 4.08961 8.01718i −7.20738 + 3.54966i
17.10 −1.40147 0.375522i −1.48402 2.60724i −1.64101 0.947435i −3.73472 3.32444i 1.10073 + 4.21124i 2.97299 + 6.33730i 6.04782 + 6.04782i −4.59537 + 7.73838i 3.98568 + 6.06157i
17.11 −1.31040 0.351121i 2.87804 + 0.846693i −1.87023 1.07978i −2.09369 + 4.54054i −3.47410 2.12005i 1.11647 + 6.91039i 5.90875 + 5.90875i 7.56622 + 4.87363i 4.33785 5.21479i
17.12 −0.667244 0.178787i −2.94454 0.574167i −3.05085 1.76141i 1.04868 + 4.88879i 1.86207 + 0.909557i 6.73061 1.92324i 3.67457 + 3.67457i 8.34066 + 3.38132i 0.174326 3.44951i
17.13 −0.161935 0.0433902i −1.19649 2.75108i −3.43976 1.98595i 4.97108 + 0.537016i 0.0743827 + 0.497410i −6.97488 0.592480i 0.945023 + 0.945023i −6.13684 + 6.58325i −0.781688 0.302658i
17.14 −0.0875643 0.0234628i 2.77616 + 1.13706i −3.45698 1.99589i 4.80744 1.37424i −0.216414 0.164703i 2.18034 6.65178i 0.512285 + 0.512285i 6.41417 + 6.31335i −0.453203 + 0.00753886i
17.15 0.0875643 + 0.0234628i 1.83570 2.37281i −3.45698 1.99589i −4.80744 + 1.37424i 0.216414 0.164703i 2.18034 6.65178i −0.512285 0.512285i −2.26044 8.71151i −0.453203 + 0.00753886i
17.16 0.161935 + 0.0433902i 0.339350 + 2.98075i −3.43976 1.98595i −4.97108 0.537016i −0.0743827 + 0.497410i −6.97488 0.592480i −0.945023 0.945023i −8.76968 + 2.02303i −0.781688 0.302658i
17.17 0.667244 + 0.178787i −2.26297 + 1.96951i −3.05085 1.76141i −1.04868 4.88879i −1.86207 + 0.909557i 6.73061 1.92324i −3.67457 3.67457i 1.24202 8.91389i 0.174326 3.44951i
17.18 1.31040 + 0.351121i 2.06911 2.17228i −1.87023 1.07978i 2.09369 4.54054i 3.47410 2.12005i 1.11647 + 6.91039i −5.90875 5.90875i −0.437576 8.98936i 4.33785 5.21479i
17.19 1.40147 + 0.375522i 0.0184202 + 2.99994i −1.64101 0.947435i 3.73472 + 3.32444i −1.10073 + 4.21124i 2.97299 + 6.33730i −6.04782 6.04782i −8.99932 + 0.110519i 3.98568 + 6.06157i
17.20 1.55206 + 0.415874i −2.99899 0.0778404i −1.22815 0.709073i −3.76090 + 3.29479i −4.62225 1.36802i −5.75785 + 3.98085i −6.15604 6.15604i 8.98788 + 0.466885i −7.20738 + 3.54966i
See next 80 embeddings (of 112 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 68.28
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.c odd 4 1 inner
7.d odd 6 1 inner
15.e even 4 1 inner
21.g even 6 1 inner
35.k even 12 1 inner
105.w odd 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.3.w.a 112
3.b odd 2 1 inner 105.3.w.a 112
5.c odd 4 1 inner 105.3.w.a 112
7.d odd 6 1 inner 105.3.w.a 112
15.e even 4 1 inner 105.3.w.a 112
21.g even 6 1 inner 105.3.w.a 112
35.k even 12 1 inner 105.3.w.a 112
105.w odd 12 1 inner 105.3.w.a 112
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.3.w.a 112 1.a even 1 1 trivial
105.3.w.a 112 3.b odd 2 1 inner
105.3.w.a 112 5.c odd 4 1 inner
105.3.w.a 112 7.d odd 6 1 inner
105.3.w.a 112 15.e even 4 1 inner
105.3.w.a 112 21.g even 6 1 inner
105.3.w.a 112 35.k even 12 1 inner
105.3.w.a 112 105.w odd 12 1 inner

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