# Properties

 Label 143.2.b Level 143 Weight 2 Character orbit b Rep. character $$\chi_{143}(12,\cdot)$$ Character field $$\Q$$ Dimension 12 Newform subspaces 1 Sturm bound 28 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$143 = 11 \cdot 13$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 143.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$13$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$28$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(143, [\chi])$$.

Total New Old
Modular forms 16 12 4
Cusp forms 12 12 0
Eisenstein series 4 0 4

## Trace form

 $$12q - 4q^{3} - 14q^{4} + 12q^{9} + O(q^{10})$$ $$12q - 4q^{3} - 14q^{4} + 12q^{9} + 8q^{10} - 8q^{13} + 10q^{16} - 12q^{17} - 2q^{22} - 4q^{23} - 16q^{25} + 10q^{26} - 28q^{27} + 8q^{29} + 4q^{30} + 16q^{35} - 16q^{36} + 18q^{38} + 4q^{39} + 16q^{40} - 2q^{42} + 12q^{43} - 58q^{48} + 32q^{49} + 36q^{52} - 20q^{53} - 8q^{55} + 22q^{56} - 12q^{61} - 72q^{62} - 10q^{64} - 20q^{65} + 2q^{66} + 68q^{68} + 52q^{69} + 20q^{74} - 8q^{75} + 8q^{77} + 6q^{78} - 48q^{79} - 36q^{81} - 44q^{82} + 12q^{87} + 30q^{88} + 68q^{90} - 6q^{92} - 64q^{94} - 4q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(143, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
143.2.b.a $$12$$ $$1.142$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ $$1 - 5 T^{2} + 17 T^{4} - 45 T^{6} + 101 T^{8} - 204 T^{10} + 412 T^{12} - 816 T^{14} + 1616 T^{16} - 2880 T^{18} + 4352 T^{20} - 5120 T^{22} + 4096 T^{24}$$
$3$ $$( 1 + 2 T + 8 T^{2} + 16 T^{3} + 45 T^{4} + 76 T^{5} + 157 T^{6} + 228 T^{7} + 405 T^{8} + 432 T^{9} + 648 T^{10} + 486 T^{11} + 729 T^{12} )^{2}$$
$5$ $$1 - 22 T^{2} + 287 T^{4} - 2722 T^{6} + 20755 T^{8} - 132344 T^{10} + 715994 T^{12} - 3308600 T^{14} + 12971875 T^{16} - 42531250 T^{18} + 112109375 T^{20} - 214843750 T^{22} + 244140625 T^{24}$$
$7$ $$1 - 58 T^{2} + 1661 T^{4} - 30904 T^{6} + 414824 T^{8} - 4224114 T^{10} + 33423324 T^{12} - 206981586 T^{14} + 995992424 T^{16} - 3635824696 T^{18} + 9575334461 T^{20} - 16383564442 T^{22} + 13841287201 T^{24}$$
$11$ $$( 1 + T^{2} )^{6}$$
$13$ $$1 + 8 T + 20 T^{2} + 40 T^{3} + 287 T^{4} + 1328 T^{5} + 4584 T^{6} + 17264 T^{7} + 48503 T^{8} + 87880 T^{9} + 571220 T^{10} + 2970344 T^{11} + 4826809 T^{12}$$
$17$ $$( 1 + 6 T + 68 T^{2} + 234 T^{3} + 1455 T^{4} + 2832 T^{5} + 19896 T^{6} + 48144 T^{7} + 420495 T^{8} + 1149642 T^{9} + 5679428 T^{10} + 8519142 T^{11} + 24137569 T^{12} )^{2}$$
$19$ $$1 - 110 T^{2} + 6849 T^{4} - 295280 T^{6} + 9707444 T^{8} - 252675522 T^{10} + 5325171464 T^{12} - 91215863442 T^{14} + 1265083809524 T^{16} - 13891707741680 T^{18} + 116320423267809 T^{20} - 674417288358110 T^{22} + 2213314919066161 T^{24}$$
$23$ $$( 1 + 2 T + 40 T^{2} - 144 T^{3} + 949 T^{4} - 2476 T^{5} + 43293 T^{6} - 56948 T^{7} + 502021 T^{8} - 1752048 T^{9} + 11193640 T^{10} + 12872686 T^{11} + 148035889 T^{12} )^{2}$$
$29$ $$( 1 - 4 T + 132 T^{2} - 532 T^{3} + 8111 T^{4} - 29224 T^{5} + 297096 T^{6} - 847496 T^{7} + 6821351 T^{8} - 12974948 T^{9} + 93361092 T^{10} - 82044596 T^{11} + 594823321 T^{12} )^{2}$$
$31$ $$1 - 210 T^{2} + 21511 T^{4} - 1461586 T^{6} + 75243131 T^{8} - 3121766748 T^{10} + 106535910906 T^{12} - 3000017844828 T^{14} + 69488611584251 T^{16} - 1297162955098066 T^{18} + 18346539106393351 T^{20} - 172121940265968210 T^{22} + 787662783788549761 T^{24}$$
$37$ $$1 - 218 T^{2} + 26207 T^{4} - 2191994 T^{6} + 139565323 T^{8} - 7059997468 T^{10} + 289296274538 T^{12} - 9665136533692 T^{14} + 261567885319003 T^{16} - 5624056894169546 T^{18} + 92051549048907647 T^{20} - 1048271393187091082 T^{22} + 6582952005840035281 T^{24}$$
$41$ $$1 - 350 T^{2} + 60137 T^{4} - 6677264 T^{6} + 532053524 T^{8} - 31989562698 T^{10} + 1486526234040 T^{12} - 53774454895338 T^{14} + 1503456098031764 T^{16} - 31717700044676624 T^{18} + 480189448503649577 T^{20} - 4697930758553340350 T^{22} + 22563490300366186081 T^{24}$$
$43$ $$( 1 - 6 T + 172 T^{2} - 1150 T^{3} + 14063 T^{4} - 92496 T^{5} + 732408 T^{6} - 3977328 T^{7} + 26002487 T^{8} - 91433050 T^{9} + 588033772 T^{10} - 882050658 T^{11} + 6321363049 T^{12} )^{2}$$
$47$ $$1 - 344 T^{2} + 56746 T^{4} - 6111480 T^{6} + 490453519 T^{8} - 31258355888 T^{10} + 1622912397580 T^{12} - 69049708156592 T^{14} + 2393256718047439 T^{16} - 65876958898876920 T^{18} + 1351195272908289706 T^{20} - 18094101489125536856 T^{22} +$$$$11\!\cdots\!41$$$$T^{24}$$
$53$ $$( 1 + 10 T + 217 T^{2} + 1476 T^{3} + 19432 T^{4} + 99010 T^{5} + 1144464 T^{6} + 5247530 T^{7} + 54584488 T^{8} + 219742452 T^{9} + 1712234377 T^{10} + 4181954930 T^{11} + 22164361129 T^{12} )^{2}$$
$59$ $$1 - 274 T^{2} + 45847 T^{4} - 5510178 T^{6} + 520879275 T^{8} - 40353433084 T^{10} + 2597499085498 T^{12} - 140470300565404 T^{14} + 6311682212593275 T^{16} - 232422248496898098 T^{18} + 6731735072845304887 T^{20} -$$$$14\!\cdots\!74$$$$T^{22} +$$$$17\!\cdots\!81$$$$T^{24}$$
$61$ $$( 1 + 6 T + 136 T^{2} + 1330 T^{3} + 13463 T^{4} + 91968 T^{5} + 1111632 T^{6} + 5610048 T^{7} + 50095823 T^{8} + 301884730 T^{9} + 1883034376 T^{10} + 5067577806 T^{11} + 51520374361 T^{12} )^{2}$$
$67$ $$1 - 294 T^{2} + 42823 T^{4} - 4204714 T^{6} + 316149251 T^{8} - 20061645312 T^{10} + 1266508121130 T^{12} - 90056725805568 T^{14} + 6370761810960371 T^{16} - 380351625923344666 T^{18} + 17389036156008037543 T^{20} -$$$$53\!\cdots\!06$$$$T^{22} +$$$$81\!\cdots\!61$$$$T^{24}$$
$71$ $$1 - 354 T^{2} + 74695 T^{4} - 11079698 T^{6} + 1290715451 T^{8} - 121403301996 T^{10} + 9475711215738 T^{12} - 611994045361836 T^{14} + 32799249302583131 T^{16} - 1419312459558935858 T^{18} + 48234560016402117895 T^{20} -$$$$11\!\cdots\!54$$$$T^{22} +$$$$16\!\cdots\!41$$$$T^{24}$$
$73$ $$1 - 642 T^{2} + 195557 T^{4} - 37725800 T^{6} + 5188402488 T^{8} - 541684076186 T^{10} + 44392042334828 T^{12} - 2886634441995194 T^{14} + 147341504259223608 T^{16} - 5709204754133556200 T^{18} +$$$$15\!\cdots\!17$$$$T^{20} -$$$$27\!\cdots\!58$$$$T^{22} +$$$$22\!\cdots\!21$$$$T^{24}$$
$79$ $$( 1 + 24 T + 604 T^{2} + 9384 T^{3} + 133959 T^{4} + 1474528 T^{5} + 14612440 T^{6} + 116487712 T^{7} + 836038119 T^{8} + 4626677976 T^{9} + 23525848924 T^{10} + 73849353576 T^{11} + 243087455521 T^{12} )^{2}$$
$83$ $$1 - 518 T^{2} + 131393 T^{4} - 21504800 T^{6} + 2572651652 T^{8} - 248777467218 T^{10} + 21398981031480 T^{12} - 1713827971664802 T^{14} + 122093727921796292 T^{16} - 7030787341225671200 T^{18} +$$$$29\!\cdots\!13$$$$T^{20} -$$$$80\!\cdots\!82$$$$T^{22} +$$$$10\!\cdots\!61$$$$T^{24}$$
$89$ $$1 - 502 T^{2} + 141807 T^{4} - 27981778 T^{6} + 4226117411 T^{8} - 509690782104 T^{10} + 50083832568410 T^{12} - 4037260685045784 T^{14} + 265156077095258051 T^{16} - 13906420153824108658 T^{18} +$$$$55\!\cdots\!67$$$$T^{20} -$$$$15\!\cdots\!02$$$$T^{22} +$$$$24\!\cdots\!21$$$$T^{24}$$
$97$ $$1 - 810 T^{2} + 313519 T^{4} - 77379274 T^{6} + 13723791611 T^{8} - 1866852082188 T^{10} + 201893417771178 T^{12} - 17565211241306892 T^{14} + 1214957403915661691 T^{16} - 64454769003730441546 T^{18} +$$$$24\!\cdots\!59$$$$T^{20} -$$$$59\!\cdots\!90$$$$T^{22} +$$$$69\!\cdots\!41$$$$T^{24}$$