Properties

Label 43.3.b
Level 43
Weight 3
Character orbit b
Rep. character \(\chi_{43}(42,\cdot)\)
Character field \(\Q\)
Dimension 7
Newform subspaces 2
Sturm bound 11
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(11\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(43, [\chi])\).

Total New Old
Modular forms 9 9 0
Cusp forms 7 7 0
Eisenstein series 2 2 0

Trace form

\( 7q - 12q^{4} + 6q^{6} - 27q^{9} + O(q^{10}) \) \( 7q - 12q^{4} + 6q^{6} - 27q^{9} - 2q^{10} + 17q^{11} + 13q^{13} + 36q^{14} + 28q^{15} - 52q^{16} - 29q^{17} + 56q^{21} - 77q^{23} + 62q^{24} - 59q^{25} - 93q^{31} + 208q^{35} - 86q^{36} + 170q^{38} + 206q^{40} - 133q^{41} - 33q^{43} - 120q^{44} - 48q^{47} + 43q^{49} - 188q^{52} - 47q^{53} - 284q^{54} - 264q^{56} + 420q^{57} + 430q^{58} - 66q^{59} - 232q^{60} + 164q^{64} - 144q^{66} + 21q^{67} - 86q^{68} - 50q^{74} + 620q^{78} + 164q^{79} + 463q^{81} + 133q^{83} + 172q^{84} - 372q^{86} - 510q^{87} - 796q^{90} + 162q^{92} - 130q^{95} + 362q^{96} - 573q^{97} - 655q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
43.3.b.a \(1\) \(1.172\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+4q^{4}+9q^{9}-21q^{11}-17q^{13}+\cdots\)
43.3.b.b \(6\) \(1.172\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-2+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 2 T )( 1 + 2 T ) \))(\( 1 - 4 T^{2} + 41 T^{4} - 114 T^{6} + 656 T^{8} - 1024 T^{10} + 4096 T^{12} \))
$3$ (\( ( 1 - 3 T )( 1 + 3 T ) \))(\( 1 - 9 T^{2} + 26 T^{4} - 254 T^{6} + 2106 T^{8} - 59049 T^{10} + 531441 T^{12} \))
$5$ (\( ( 1 - 5 T )( 1 + 5 T ) \))(\( 1 - 33 T^{2} + 1538 T^{4} - 41006 T^{6} + 961250 T^{8} - 12890625 T^{10} + 244140625 T^{12} \))
$7$ (\( ( 1 - 7 T )( 1 + 7 T ) \))(\( 1 - 144 T^{2} + 11511 T^{4} - 668464 T^{6} + 27637911 T^{8} - 830131344 T^{10} + 13841287201 T^{12} \))
$11$ (\( 1 + 21 T + 121 T^{2} \))(\( ( 1 - 19 T + 411 T^{2} - 4354 T^{3} + 49731 T^{4} - 278179 T^{5} + 1771561 T^{6} )^{2} \))
$13$ (\( 1 + 17 T + 169 T^{2} \))(\( ( 1 - 15 T + 257 T^{2} - 1570 T^{3} + 43433 T^{4} - 428415 T^{5} + 4826809 T^{6} )^{2} \))
$17$ (\( 1 + 9 T + 289 T^{2} \))(\( ( 1 + 10 T + 767 T^{2} + 5655 T^{3} + 221663 T^{4} + 835210 T^{5} + 24137569 T^{6} )^{2} \))
$19$ (\( ( 1 - 19 T )( 1 + 19 T ) \))(\( 1 - 691 T^{2} + 378040 T^{4} - 133433020 T^{6} + 49266550840 T^{8} - 11735642061331 T^{10} + 2213314919066161 T^{12} \))
$23$ (\( 1 - 3 T + 529 T^{2} \))(\( ( 1 + 40 T + 1387 T^{2} + 28195 T^{3} + 733723 T^{4} + 11193640 T^{5} + 148035889 T^{6} )^{2} \))
$29$ (\( ( 1 - 29 T )( 1 + 29 T ) \))(\( 1 - 1621 T^{2} + 1946890 T^{4} - 2007466870 T^{6} + 1376998306090 T^{8} - 810899435409781 T^{10} + 353814783205469041 T^{12} \))
$31$ (\( 1 - 19 T + 961 T^{2} \))(\( ( 1 + 56 T + 2591 T^{2} + 96591 T^{3} + 2489951 T^{4} + 51717176 T^{5} + 887503681 T^{6} )^{2} \))
$37$ (\( ( 1 - 37 T )( 1 + 37 T ) \))(\( 1 - 5259 T^{2} + 14237096 T^{4} - 24083763884 T^{6} + 26682610076456 T^{8} - 18472129448170539 T^{10} + 6582952005840035281 T^{12} \))
$41$ (\( 1 - 39 T + 1681 T^{2} \))(\( ( 1 + 86 T + 6451 T^{2} + 292121 T^{3} + 10844131 T^{4} + 243015446 T^{5} + 4750104241 T^{6} )^{2} \))
$43$ (\( 1 + 43 T \))(\( 1 - 10 T + 147 T^{2} + 135020 T^{3} + 271803 T^{4} - 34188010 T^{5} + 6321363049 T^{6} \))
$47$ (\( 1 + 78 T + 2209 T^{2} \))(\( ( 1 - 15 T + 5052 T^{2} - 79770 T^{3} + 11159868 T^{4} - 73195215 T^{5} + 10779215329 T^{6} )^{2} \))
$53$ (\( 1 - 63 T + 2809 T^{2} \))(\( ( 1 + 55 T + 4677 T^{2} + 168490 T^{3} + 13137693 T^{4} + 433976455 T^{5} + 22164361129 T^{6} )^{2} \))
$59$ (\( 1 + 54 T + 3481 T^{2} \))(\( ( 1 + 6 T + 4271 T^{2} + 147196 T^{3} + 14867351 T^{4} + 72704166 T^{5} + 42180533641 T^{6} )^{2} \))
$61$ (\( ( 1 - 61 T )( 1 + 61 T ) \))(\( 1 - 6176 T^{2} + 53251015 T^{4} - 178029474320 T^{6} + 737305086778615 T^{8} - 1183984365071207456 T^{10} + \)\(26\!\cdots\!21\)\( T^{12} \))
$67$ (\( 1 - 91 T + 4489 T^{2} \))(\( ( 1 + 35 T + 9017 T^{2} + 350730 T^{3} + 40477313 T^{4} + 705289235 T^{5} + 90458382169 T^{6} )^{2} \))
$71$ (\( ( 1 - 71 T )( 1 + 71 T ) \))(\( 1 - 22246 T^{2} + 239223215 T^{4} - 1523736510420 T^{6} + 6079064027374415 T^{8} - 14365433056093199206 T^{10} + \)\(16\!\cdots\!41\)\( T^{12} \))
$73$ (\( ( 1 - 73 T )( 1 + 73 T ) \))(\( 1 - 24604 T^{2} + 277197791 T^{4} - 1859020745064 T^{6} + 7871929673485631 T^{8} - 19842144100961968924 T^{10} + \)\(22\!\cdots\!21\)\( T^{12} \))
$79$ (\( 1 + 14 T + 6241 T^{2} \))(\( ( 1 - 89 T + 20896 T^{2} - 1122134 T^{3} + 130411936 T^{4} - 3466557209 T^{5} + 243087455521 T^{6} )^{2} \))
$83$ (\( 1 - 123 T + 6889 T^{2} \))(\( ( 1 - 5 T + 14767 T^{2} - 128390 T^{3} + 101729863 T^{4} - 237291605 T^{5} + 326940373369 T^{6} )^{2} \))
$89$ (\( ( 1 - 89 T )( 1 + 89 T ) \))(\( 1 - 38876 T^{2} + 668902015 T^{4} - 6712320081320 T^{6} + 41968411430515615 T^{8} - \)\(15\!\cdots\!56\)\( T^{10} + \)\(24\!\cdots\!21\)\( T^{12} \))
$97$ (\( 1 + 193 T + 9409 T^{2} \))(\( ( 1 + 190 T + 26827 T^{2} + 2529295 T^{3} + 252415243 T^{4} + 16820563390 T^{5} + 832972004929 T^{6} )^{2} \))
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