Properties

Label 105.4.q.b
Level $105$
Weight $4$
Character orbit 105.q
Analytic conductor $6.195$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 44q + 62q^{4} - 4q^{5} + 108q^{6} + 198q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 44q + 62q^{4} - 4q^{5} + 108q^{6} + 198q^{9} - 92q^{10} - 174q^{11} + 254q^{14} + 48q^{15} - 262q^{16} + 38q^{19} - 816q^{20} - 174q^{21} + 558q^{24} - 24q^{25} - 586q^{26} - 1024q^{29} + 84q^{30} - 912q^{31} + 1112q^{34} - 690q^{35} + 1116q^{36} - 390q^{39} + 552q^{40} - 356q^{41} + 1114q^{44} + 36q^{45} + 1502q^{46} + 24q^{49} + 5768q^{50} - 516q^{51} + 486q^{54} + 2444q^{55} + 972q^{56} + 2200q^{59} + 216q^{60} - 1068q^{61} - 13180q^{64} - 154q^{65} - 390q^{66} - 1356q^{69} - 5870q^{70} + 4392q^{71} - 2342q^{74} - 576q^{75} - 4948q^{76} - 464q^{79} - 5588q^{80} - 1782q^{81} + 4278q^{84} + 6880q^{85} - 2948q^{86} + 5684q^{89} - 1656q^{90} - 4192q^{91} + 8762q^{94} + 5212q^{95} - 5778q^{96} - 3132q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4.1 −4.85916 + 2.80544i −2.59808 1.50000i 11.7410 20.3360i 2.40235 10.9192i 16.8326 −9.44251 15.9323i 86.8672i 4.50000 + 7.79423i 18.9597 + 59.7978i
4.2 −4.10597 + 2.37058i −2.59808 1.50000i 7.23930 12.5388i −2.66182 + 10.8589i 14.2235 15.6813 + 9.85381i 30.7161i 4.50000 + 7.79423i −14.8124 50.8961i
4.3 −3.89316 + 2.24772i 2.59808 + 1.50000i 6.10447 10.5732i −0.533135 11.1676i −13.4863 −3.71892 + 18.1430i 18.9210i 4.50000 + 7.79423i 27.1772 + 42.2790i
4.4 −3.00489 + 1.73487i −2.59808 1.50000i 2.01958 3.49802i −10.2956 4.35891i 10.4092 −12.4845 + 13.6798i 13.7431i 4.50000 + 7.79423i 38.4994 4.76357i
4.5 −2.89323 + 1.67041i −2.59808 1.50000i 1.58052 2.73755i 9.21296 + 6.33414i 10.0224 −6.15758 17.4667i 16.1660i 4.50000 + 7.79423i −37.2358 2.93674i
4.6 −2.21373 + 1.27810i 2.59808 + 1.50000i −0.732945 + 1.26950i 5.74885 9.58910i −7.66857 −2.98784 18.2777i 24.1966i 4.50000 + 7.79423i −0.470588 + 28.5752i
4.7 −2.01833 + 1.16528i 2.59808 + 1.50000i −1.28423 + 2.22435i 7.90497 + 7.90642i −6.99170 18.1257 + 3.80267i 24.6305i 4.50000 + 7.79423i −25.1681 6.74622i
4.8 −1.96118 + 1.13229i 2.59808 + 1.50000i −1.43586 + 2.48698i −5.60388 + 9.67453i −6.79371 −18.1088 3.88231i 24.6198i 4.50000 + 7.79423i 0.0358556 25.3186i
4.9 −1.50072 + 0.866440i −2.59808 1.50000i −2.49856 + 4.32764i 10.6609 3.36827i 5.19864 −14.9159 + 10.9780i 22.5225i 4.50000 + 7.79423i −13.0806 + 14.2919i
4.10 −0.761268 + 0.439518i −2.59808 1.50000i −3.61365 + 6.25902i 0.571597 11.1657i 2.63711 18.5184 0.260966i 13.3854i 4.50000 + 7.79423i 4.47240 + 8.75133i
4.11 −0.755385 + 0.436122i −2.59808 1.50000i −3.61960 + 6.26932i −7.84576 + 7.96518i 2.61673 10.7711 15.0659i 13.2923i 4.50000 + 7.79423i 2.45278 9.43848i
4.12 0.755385 0.436122i 2.59808 + 1.50000i −3.61960 + 6.26932i 10.8209 2.81204i 2.61673 −10.7711 + 15.0659i 13.2923i 4.50000 + 7.79423i 6.94757 6.84341i
4.13 0.761268 0.439518i 2.59808 + 1.50000i −3.61365 + 6.25902i −9.95559 5.08784i 2.63711 −18.5184 + 0.260966i 13.3854i 4.50000 + 7.79423i −9.81508 + 0.502454i
4.14 1.50072 0.866440i 2.59808 + 1.50000i −2.49856 + 4.32764i −8.24745 + 7.54848i 5.19864 14.9159 10.9780i 22.5225i 4.50000 + 7.79423i −5.83680 + 18.4741i
4.15 1.96118 1.13229i −2.59808 1.50000i −1.43586 + 2.48698i 11.1803 0.0158333i −6.79371 18.1088 + 3.88231i 24.6198i 4.50000 + 7.79423i 21.9087 12.6904i
4.16 2.01833 1.16528i −2.59808 1.50000i −1.28423 + 2.22435i 2.89467 + 10.7991i −6.99170 −18.1257 3.80267i 24.6305i 4.50000 + 7.79423i 18.4264 + 18.4231i
4.17 2.21373 1.27810i −2.59808 1.50000i −0.732945 + 1.26950i −11.1788 + 0.184097i −7.66857 2.98784 + 18.2777i 24.1966i 4.50000 + 7.79423i −24.5116 + 14.6951i
4.18 2.89323 1.67041i 2.59808 + 1.50000i 1.58052 2.73755i 0.879049 + 11.1457i 10.0224 6.15758 + 17.4667i 16.1660i 4.50000 + 7.79423i 21.1612 + 30.7788i
4.19 3.00489 1.73487i 2.59808 + 1.50000i 2.01958 3.49802i 1.37289 11.0957i 10.4092 12.4845 13.6798i 13.7431i 4.50000 + 7.79423i −15.1243 35.7232i
4.20 3.89316 2.24772i −2.59808 1.50000i 6.10447 10.5732i −9.40488 6.04552i −13.4863 3.71892 18.1430i 18.9210i 4.50000 + 7.79423i −50.2033 2.39667i
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 79.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
7.c even 3 1 inner
35.j even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.4.q.b 44
5.b even 2 1 inner 105.4.q.b 44
7.c even 3 1 inner 105.4.q.b 44
35.j even 6 1 inner 105.4.q.b 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.4.q.b 44 1.a even 1 1 trivial
105.4.q.b 44 5.b even 2 1 inner
105.4.q.b 44 7.c even 3 1 inner
105.4.q.b 44 35.j even 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(17\!\cdots\!32\)\( T_{2}^{28} - \)\(19\!\cdots\!52\)\( T_{2}^{26} + \)\(18\!\cdots\!20\)\( T_{2}^{24} - \)\(14\!\cdots\!52\)\( T_{2}^{22} + \)\(91\!\cdots\!48\)\( T_{2}^{20} - \)\(47\!\cdots\!28\)\( T_{2}^{18} + \)\(19\!\cdots\!96\)\( T_{2}^{16} - \)\(66\!\cdots\!60\)\( T_{2}^{14} + \)\(17\!\cdots\!48\)\( T_{2}^{12} - \)\(34\!\cdots\!24\)\( T_{2}^{10} + \)\(50\!\cdots\!20\)\( T_{2}^{8} - \)\(48\!\cdots\!40\)\( T_{2}^{6} + \)\(34\!\cdots\!84\)\( T_{2}^{4} - \)\(14\!\cdots\!32\)\( T_{2}^{2} + \)\(38\!\cdots\!16\)\( \)">\(T_{2}^{44} - \cdots\) acting on \(S_{4}^{\mathrm{new}}(105, [\chi])\).