Properties

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

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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.

\(\operatorname{Tr}(f)(q) = \) \( 30 q - 6 q^{2} + 6 q^{3} - 12 q^{4} + 10 q^{5} + 12 q^{6} + 107 q^{7} - 24 q^{8} - 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 30 q - 6 q^{2} + 6 q^{3} - 12 q^{4} + 10 q^{5} + 12 q^{6} + 107 q^{7} - 24 q^{8} - 63 q^{9} + 20 q^{10} + 64 q^{11} - 20 q^{12} + 8 q^{13} + 16 q^{14} + 252 q^{15} - 48 q^{16} - 126 q^{17} - 126 q^{18} + 123 q^{19} - 136 q^{20} - 514 q^{21} - 356 q^{22} - 507 q^{23} + 48 q^{24} - 419 q^{25} - 94 q^{26} - 657 q^{27} + 32 q^{28} + 757 q^{29} + 240 q^{30} + 840 q^{31} - 96 q^{32} + 1948 q^{33} + 936 q^{34} - 785 q^{35} - 164 q^{36} - 444 q^{37} + 554 q^{38} + 1954 q^{39} + 80 q^{40} - 771 q^{41} + 72 q^{42} - 789 q^{43} + 256 q^{44} - 2596 q^{45} + 1230 q^{46} - 1748 q^{47} - 80 q^{48} - 720 q^{49} - 2026 q^{50} + 1641 q^{51} + 472 q^{52} - 785 q^{53} + 2030 q^{54} + 967 q^{55} + 856 q^{56} + 5918 q^{57} + 1052 q^{58} + 2307 q^{59} - 444 q^{60} + 877 q^{61} - 278 q^{62} - 5708 q^{63} - 192 q^{64} - 3846 q^{65} - 4156 q^{66} + 1763 q^{67} - 2528 q^{68} - 1970 q^{69} - 3968 q^{70} - 6362 q^{71} - 152 q^{72} - 3584 q^{73} - 888 q^{74} + 3143 q^{75} + 360 q^{76} + 6347 q^{77} - 1460 q^{78} + 2642 q^{79} + 864 q^{80} + 1043 q^{81} + 5542 q^{82} - 372 q^{83} + 2212 q^{84} + 5136 q^{85} - 2326 q^{86} + 5451 q^{87} - 104 q^{88} - 4283 q^{89} + 5104 q^{90} - 6182 q^{91} - 92 q^{92} - 8734 q^{93} - 2550 q^{94} + 9449 q^{95} + 192 q^{96} + 7599 q^{97} + 3928 q^{98} + 1377 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −2.19033 + 4.79615i −3.83797 + 1.12693i 13.4347 15.5044i 10.1181 + 2.97094i 23.9800 15.4110i 3.32332 + 7.27706i −0.524312 0.605089i −34.5171 22.1828i
3.2 −0.284630 1.97964i −1.97837 + 4.33203i −3.83797 + 1.12693i −7.35113 + 8.48366i 9.13898 + 2.68345i −14.4370 + 9.27813i 3.32332 + 7.27706i 2.82871 + 3.26450i 18.8870 + 12.1379i
3.3 −0.284630 1.97964i 2.88906 6.32617i −3.83797 + 1.12693i 3.38697 3.90877i −13.3459 3.91870i −8.19404 + 5.26599i 3.32332 + 7.27706i −13.9925 16.1482i −8.70200 5.59244i
9.1 −1.91899 + 0.563465i −4.45973 5.14680i 3.36501 2.16256i 1.49104 + 10.3704i 11.4582 + 7.36374i −12.8017 + 28.0319i −5.23889 + 6.04600i −2.75788 + 19.1815i −8.70468 19.0606i
9.2 −1.91899 + 0.563465i −1.12472 1.29799i 3.36501 2.16256i 0.231505 + 1.61016i 2.88969 + 1.85709i 13.5480 29.6661i −5.23889 + 6.04600i 3.42270 23.8054i −1.35152 2.95942i
9.3 −1.91899 + 0.563465i 5.41593 + 6.25032i 3.36501 2.16256i 0.0474277 + 0.329867i −13.9149 8.94259i −3.79922 + 8.31912i −5.23889 + 6.04600i −5.89167 + 40.9775i −0.276882 0.606286i
13.1 −1.30972 1.51150i −4.75375 3.05505i −0.569259 + 3.95929i −6.73761 + 14.7533i 1.60838 + 11.1865i 22.9137 + 6.72806i 6.73003 4.32513i 2.04859 + 4.48580i 31.1240 9.13883i
13.2 −1.30972 1.51150i 2.05539 + 1.32092i −0.569259 + 3.95929i 5.37705 11.7741i −0.695419 4.83675i 20.2076 + 5.93348i 6.73003 4.32513i −8.73641 19.1301i −24.8390 + 7.29338i
13.3 −1.30972 1.51150i 7.02888 + 4.51719i −0.569259 + 3.95929i −7.76566 + 17.0044i −2.37815 16.5404i −9.77224 2.86939i 6.73003 4.32513i 17.7839 + 38.9414i 35.8730 10.5333i
25.1 1.68251 + 1.08128i −1.15980 8.06660i 1.66166 + 3.63853i −1.44423 0.424065i 6.77089 14.8262i 22.1855 25.6034i −1.13852 + 7.91857i −37.8186 + 11.1045i −1.97140 2.27512i
25.2 1.68251 + 1.08128i 0.0135219 + 0.0940468i 1.66166 + 3.63853i 11.1631 + 3.27779i −0.0789404 + 0.172855i −6.36931 + 7.35057i −1.13852 + 7.91857i 25.8976 7.60424i 15.2378 + 17.5854i
25.3 1.68251 + 1.08128i 1.01294 + 7.04516i 1.66166 + 3.63853i −7.67379 2.25323i −5.91352 + 12.9488i 4.19793 4.84467i −1.13852 + 7.91857i −22.7019 + 6.66587i −10.4748 12.0886i
27.1 0.830830 + 1.81926i −5.88717 + 1.72863i −2.61944 + 3.02300i −11.4083 7.33168i −8.03607 9.27412i −0.0110854 0.0771003i −7.67594 2.25386i 8.95675 5.75615i 3.85989 26.8461i
27.2 0.830830 + 1.81926i −0.858963 + 0.252214i −2.61944 + 3.02300i 9.50458 + 6.10822i −1.17250 1.35313i 3.59878 + 25.0301i −7.67594 2.25386i −22.0396 + 14.1640i −3.21578 + 22.3662i
27.3 0.830830 + 1.81926i 6.99711 2.05454i −2.61944 + 3.02300i 2.74437 + 1.76370i 9.55115 + 11.0226i −1.74684 12.1495i −7.67594 2.25386i 22.0245 14.1543i −0.928530 + 6.45807i
29.1 0.830830 1.81926i −5.88717 1.72863i −2.61944 3.02300i −11.4083 + 7.33168i −8.03607 + 9.27412i −0.0110854 + 0.0771003i −7.67594 + 2.25386i 8.95675 + 5.75615i 3.85989 + 26.8461i
29.2 0.830830 1.81926i −0.858963 0.252214i −2.61944 3.02300i 9.50458 6.10822i −1.17250 + 1.35313i 3.59878 25.0301i −7.67594 + 2.25386i −22.0396 14.1640i −3.21578 22.3662i
29.3 0.830830 1.81926i 6.99711 + 2.05454i −2.61944 3.02300i 2.74437 1.76370i 9.55115 11.0226i −1.74684 + 12.1495i −7.67594 + 2.25386i 22.0245 + 14.1543i −0.928530 6.45807i
31.1 −0.284630 + 1.97964i −2.19033 4.79615i −3.83797 1.12693i 13.4347 + 15.5044i 10.1181 2.97094i 23.9800 + 15.4110i 3.32332 7.27706i −0.524312 + 0.605089i −34.5171 + 22.1828i
31.2 −0.284630 + 1.97964i −1.97837 4.33203i −3.83797 1.12693i −7.35113 8.48366i 9.13898 2.68345i −14.4370 9.27813i 3.32332 7.27706i 2.82871 3.26450i 18.8870 12.1379i
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 41.3
Significant digits:
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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.a 30
23.c even 11 1 inner 46.4.c.a 30
23.c even 11 1 1058.4.a.v 15
23.d odd 22 1 1058.4.a.w 15
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
46.4.c.a 30 1.a even 1 1 trivial
46.4.c.a 30 23.c even 11 1 inner
1058.4.a.v 15 23.c even 11 1
1058.4.a.w 15 23.d odd 22 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{30} - 6 T_{3}^{29} + 90 T_{3}^{28} - 357 T_{3}^{27} + 4939 T_{3}^{26} - 81 T_{3}^{25} + 230139 T_{3}^{24} - 43439 T_{3}^{23} + 9691934 T_{3}^{22} + 39995486 T_{3}^{21} + 370419648 T_{3}^{20} + \cdots + 18\!\cdots\!61 \) acting on \(S_{4}^{\mathrm{new}}(46, [\chi])\). Copy content Toggle raw display