# 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

# Related objects

## 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

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