Properties

 Label 46.4.c.b Level $46$ Weight $4$ Character orbit 46.c Analytic conductor $2.714$ Analytic rank $0$ Dimension $30$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$46 = 2 \cdot 23$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 46.c (of order $$11$$, degree $$10$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$2.71408786026$$ Analytic rank: $$0$$ Dimension: $$30$$ Relative dimension: $$3$$ over $$\Q(\zeta_{11})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9}+O(q^{10})$$ 30 * q + 6 * q^2 + 2 * q^3 - 12 * q^4 - 4 * q^6 - 115 * q^7 + 24 * q^8 - 83 * q^9 $$\operatorname{Tr}(f)(q) =$$ $$30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9} - 30 q^{11} + 52 q^{12} + 104 q^{13} - 56 q^{14} + 492 q^{15} - 48 q^{16} + 274 q^{17} + 166 q^{18} - 381 q^{19} - 176 q^{20} - 546 q^{21} + 60 q^{22} - 461 q^{23} - 16 q^{24} - 363 q^{25} - 318 q^{26} + 929 q^{27} + 112 q^{28} - 41 q^{29} + 776 q^{30} + 416 q^{31} + 96 q^{32} - 960 q^{33} - 416 q^{34} + 1671 q^{35} - 420 q^{36} + 1338 q^{37} - 118 q^{38} - 1642 q^{39} - 263 q^{41} - 8 q^{42} - 561 q^{43} - 120 q^{44} - 48 q^{45} - 1322 q^{46} - 1508 q^{47} + 208 q^{48} - 304 q^{49} + 1298 q^{50} - 1313 q^{51} - 24 q^{52} + 337 q^{53} + 1222 q^{54} + 4597 q^{55} + 920 q^{56} + 3446 q^{57} + 500 q^{58} + 1507 q^{59} + 516 q^{60} - 1291 q^{61} - 590 q^{62} + 1108 q^{63} - 192 q^{64} - 2522 q^{65} - 1204 q^{66} - 5093 q^{67} - 576 q^{68} - 5786 q^{69} - 2000 q^{70} + 850 q^{71} - 1800 q^{72} + 2452 q^{73} - 2676 q^{74} + 1267 q^{75} - 512 q^{76} - 6123 q^{77} + 2272 q^{78} + 536 q^{79} + 704 q^{80} + 3083 q^{81} - 1542 q^{82} + 7180 q^{83} + 2612 q^{84} + 1126 q^{85} + 6182 q^{86} - 7541 q^{87} + 856 q^{88} + 3457 q^{89} - 300 q^{90} + 4134 q^{91} + 92 q^{92} + 4930 q^{93} + 1542 q^{94} - 9721 q^{95} - 64 q^{96} + 4159 q^{97} + 2192 q^{98} + 7587 q^{99}+O(q^{100})$$ 30 * q + 6 * q^2 + 2 * q^3 - 12 * q^4 - 4 * q^6 - 115 * q^7 + 24 * q^8 - 83 * q^9 - 30 * q^11 + 52 * q^12 + 104 * q^13 - 56 * q^14 + 492 * q^15 - 48 * q^16 + 274 * q^17 + 166 * q^18 - 381 * q^19 - 176 * q^20 - 546 * q^21 + 60 * q^22 - 461 * q^23 - 16 * q^24 - 363 * q^25 - 318 * q^26 + 929 * q^27 + 112 * q^28 - 41 * q^29 + 776 * q^30 + 416 * q^31 + 96 * q^32 - 960 * q^33 - 416 * q^34 + 1671 * q^35 - 420 * q^36 + 1338 * q^37 - 118 * q^38 - 1642 * q^39 - 263 * q^41 - 8 * q^42 - 561 * q^43 - 120 * q^44 - 48 * q^45 - 1322 * q^46 - 1508 * q^47 + 208 * q^48 - 304 * q^49 + 1298 * q^50 - 1313 * q^51 - 24 * q^52 + 337 * q^53 + 1222 * q^54 + 4597 * q^55 + 920 * q^56 + 3446 * q^57 + 500 * q^58 + 1507 * q^59 + 516 * q^60 - 1291 * q^61 - 590 * q^62 + 1108 * q^63 - 192 * q^64 - 2522 * q^65 - 1204 * q^66 - 5093 * q^67 - 576 * q^68 - 5786 * q^69 - 2000 * q^70 + 850 * q^71 - 1800 * q^72 + 2452 * q^73 - 2676 * q^74 + 1267 * q^75 - 512 * q^76 - 6123 * q^77 + 2272 * q^78 + 536 * q^79 + 704 * q^80 + 3083 * q^81 - 1542 * q^82 + 7180 * q^83 + 2612 * q^84 + 1126 * q^85 + 6182 * q^86 - 7541 * q^87 + 856 * q^88 + 3457 * q^89 - 300 * q^90 + 4134 * q^91 + 92 * q^92 + 4930 * q^93 + 1542 * q^94 - 9721 * q^95 - 64 * q^96 + 4159 * q^97 + 2192 * q^98 + 7587 * q^99

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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
3.1 0.284630 + 1.97964i −3.62606 + 7.93996i −3.83797 + 1.12693i 6.91905 7.98501i −16.7504 4.91835i −16.1046 + 10.3498i −3.32332 7.27706i −32.2134 37.1762i 17.7768 + 11.4245i
3.2 0.284630 + 1.97964i −0.493326 + 1.08023i −3.83797 + 1.12693i −10.8228 + 12.4902i −2.27889 0.669143i 0.379417 0.243837i −3.32332 7.27706i 16.7577 + 19.3394i −27.8066 17.8702i
3.3 0.284630 + 1.97964i 2.60327 5.70036i −3.83797 + 1.12693i 6.82565 7.87722i 12.0256 + 3.53105i 9.96901 6.40669i −3.32332 7.27706i −8.03584 9.27386i 17.5369 + 11.2703i
9.1 1.91899 0.563465i −3.58705 4.13968i 3.36501 2.16256i −1.27675 8.88002i −9.21607 5.92281i 1.52711 3.34391i 5.23889 6.04600i −0.427496 + 2.97330i −7.45366 16.3212i
9.2 1.91899 0.563465i 1.58551 + 1.82978i 3.36501 2.16256i 2.65345 + 18.4552i 4.07359 + 2.61794i 8.33333 18.2475i 5.23889 6.04600i 3.00826 20.9229i 15.4908 + 33.9201i
9.3 1.91899 0.563465i 4.34636 + 5.01597i 3.36501 2.16256i −1.02987 7.16288i 11.1669 + 7.17655i −7.28047 + 15.9420i 5.23889 6.04600i −2.42659 + 16.8773i −6.01233 13.1652i
13.1 1.30972 + 1.51150i −7.37753 4.74125i −0.569259 + 3.95929i −7.38096 + 16.1620i −2.49611 17.3608i −23.1426 6.79527i −6.73003 + 4.32513i 20.7323 + 45.3973i −34.0959 + 10.0115i
13.2 1.30972 + 1.51150i 2.26977 + 1.45869i −0.569259 + 3.95929i −3.30726 + 7.24189i 0.767954 + 5.34124i 19.2136 + 5.64162i −6.73003 + 4.32513i −8.19213 17.9383i −15.2777 + 4.48594i
13.3 1.30972 + 1.51150i 7.23466 + 4.64943i −0.569259 + 3.95929i 5.71615 12.5166i 2.44777 + 17.0246i −32.6087 9.57479i −6.73003 + 4.32513i 19.5068 + 42.7140i 26.4054 7.75334i
25.1 −1.68251 1.08128i −1.28869 8.96304i 1.66166 + 3.63853i −3.51873 1.03319i −7.52334 + 16.4738i −6.62723 + 7.64823i 1.13852 7.91857i −52.7690 + 15.4944i 4.80311 + 5.54308i
25.2 −1.68251 1.08128i 0.0510239 + 0.354879i 1.66166 + 3.63853i 8.79133 + 2.58137i 0.297876 0.652258i 10.6913 12.3384i 1.13852 7.91857i 25.7830 7.57056i −12.0003 13.8491i
25.3 −1.68251 1.08128i 0.625435 + 4.35000i 1.66166 + 3.63853i −12.8224 3.76500i 3.65127 7.99517i −19.0515 + 21.9866i 1.13852 7.91857i 7.37501 2.16550i 17.5028 + 20.1993i
27.1 −0.830830 1.81926i −4.95549 + 1.45506i −2.61944 + 3.02300i 5.53427 + 3.55666i 6.76431 + 7.80643i 4.17332 + 29.0261i 7.67594 + 2.25386i −0.274197 + 0.176216i 1.87247 13.0233i
27.2 −0.830830 1.81926i −0.430531 + 0.126415i −2.61944 + 3.02300i −13.5914 8.73463i 0.587680 + 0.678219i −2.74097 19.0638i 7.67594 + 2.25386i −22.5445 + 14.4885i −4.59850 + 31.9833i
27.3 −0.830830 1.81926i 4.04264 1.18703i −2.61944 + 3.02300i 17.3103 + 11.1246i −5.51826 6.36842i −4.23099 29.4272i 7.67594 + 2.25386i −7.77992 + 4.99985i 5.85675 40.7346i
29.1 −0.830830 + 1.81926i −4.95549 1.45506i −2.61944 3.02300i 5.53427 3.55666i 6.76431 7.80643i 4.17332 29.0261i 7.67594 2.25386i −0.274197 0.176216i 1.87247 + 13.0233i
29.2 −0.830830 + 1.81926i −0.430531 0.126415i −2.61944 3.02300i −13.5914 + 8.73463i 0.587680 0.678219i −2.74097 + 19.0638i 7.67594 2.25386i −22.5445 14.4885i −4.59850 31.9833i
29.3 −0.830830 + 1.81926i 4.04264 + 1.18703i −2.61944 3.02300i 17.3103 11.1246i −5.51826 + 6.36842i −4.23099 + 29.4272i 7.67594 2.25386i −7.77992 4.99985i 5.85675 + 40.7346i
31.1 0.284630 1.97964i −3.62606 7.93996i −3.83797 1.12693i 6.91905 + 7.98501i −16.7504 + 4.91835i −16.1046 10.3498i −3.32332 + 7.27706i −32.2134 + 37.1762i 17.7768 11.4245i
31.2 0.284630 1.97964i −0.493326 1.08023i −3.83797 1.12693i −10.8228 12.4902i −2.27889 + 0.669143i 0.379417 + 0.243837i −3.32332 + 7.27706i 16.7577 19.3394i −27.8066 + 17.8702i
See all 30 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 41.3 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 46.4.c.b 30
23.c even 11 1 inner 46.4.c.b 30
23.c even 11 1 1058.4.a.u 15
23.d odd 22 1 1058.4.a.t 15

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
46.4.c.b 30 1.a even 1 1 trivial
46.4.c.b 30 23.c even 11 1 inner
1058.4.a.t 15 23.d odd 22 1
1058.4.a.u 15 23.c even 11 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{3}^{30} - 2 T_{3}^{29} + 84 T_{3}^{28} - 511 T_{3}^{27} + 6667 T_{3}^{26} - 11781 T_{3}^{25} + 604763 T_{3}^{24} - 2379383 T_{3}^{23} + 36745868 T_{3}^{22} - 169950272 T_{3}^{21} + \cdots + 26\!\cdots\!29$$ acting on $$S_{4}^{\mathrm{new}}(46, [\chi])$$.