# Properties

 Label 24.8.f Level 24 Weight 8 Character orbit f Rep. character $$\chi_{24}(11,\cdot)$$ Character field $$\Q$$ Dimension 26 Newform subspaces 3 Sturm bound 32 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ = $$8$$ Character orbit: $$[\chi]$$ = 24.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$24$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$32$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(24, [\chi])$$.

Total New Old
Modular forms 30 30 0
Cusp forms 26 26 0
Eisenstein series 4 4 0

## Trace form

 $$26q - 2q^{3} - 28q^{4} + 40q^{6} - 2q^{9} + O(q^{10})$$ $$26q - 2q^{3} - 28q^{4} + 40q^{6} - 2q^{9} - 5304q^{10} - 12812q^{12} - 14872q^{16} - 9800q^{18} + 60580q^{19} - 82496q^{22} - 81080q^{24} + 281246q^{25} + 238042q^{27} - 50352q^{28} - 24624q^{30} - 45136q^{33} - 332816q^{34} - 148244q^{36} + 115872q^{40} + 331272q^{42} - 752852q^{43} + 378144q^{46} + 566200q^{48} - 2158138q^{49} - 1112848q^{51} + 1542144q^{52} + 26104q^{54} - 347548q^{57} + 2501160q^{58} + 414000q^{60} - 728272q^{64} - 91288q^{66} + 1552540q^{67} + 5522736q^{70} + 3503824q^{72} + 1267060q^{73} + 573562q^{75} - 213032q^{76} - 10346544q^{78} + 6421738q^{81} - 17006144q^{82} - 12156480q^{84} - 17283152q^{88} + 14281704q^{90} + 4997664q^{91} - 2342208q^{94} + 7955728q^{96} + 13155724q^{97} + 14430800q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(24, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
24.8.f.a $$2$$ $$7.497$$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$-86$$ $$0$$ $$0$$ $$q+8\beta q^{2}+(-43+13\beta )q^{3}-2^{7}q^{4}+\cdots$$
24.8.f.b $$4$$ $$7.497$$ $$\Q(\sqrt{6}, \sqrt{-26})$$ None $$0$$ $$-36$$ $$0$$ $$0$$ $$q+(2\beta _{1}+\beta _{2})q^{2}+(-9-9\beta _{1})q^{3}+(-80+\cdots)q^{4}+\cdots$$
24.8.f.c $$20$$ $$7.497$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$120$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(6+\beta _{1}-\beta _{4})q^{3}+(3^{3}+\beta _{3}+\cdots)q^{4}+\cdots$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 + 128 T^{2}$$)($$1 + 160 T^{2} + 16384 T^{4}$$)($$1 - 274 T^{2} + 45864 T^{4} - 5031360 T^{6} + 776389632 T^{8} - 102828146688 T^{10} + 12720367730688 T^{12} - 1350595415900160 T^{14} + 201712005185273856 T^{16} - 19743780766392254464 T^{18} +$$$$11\!\cdots\!24$$$$T^{20}$$)
$3$ ($$1 + 86 T + 2187 T^{2}$$)($$( 1 + 18 T + 2187 T^{2} )^{2}$$)($$( 1 - 60 T + 531 T^{2} + 25920 T^{3} + 766422 T^{4} - 160875720 T^{5} + 1676164914 T^{6} + 123974556480 T^{7} + 5554447550793 T^{8} - 1372607547297660 T^{9} + 50031545098999707 T^{10} )^{2}$$)
$5$ ($$( 1 + 78125 T^{2} )^{2}$$)($$( 1 + 146650 T^{2} + 6103515625 T^{4} )^{2}$$)($$( 1 + 212726 T^{2} + 34462341957 T^{4} + 4087236092863080 T^{6} +$$$$39\!\cdots\!50$$$$T^{8} +$$$$34\!\cdots\!00$$$$T^{10} +$$$$24\!\cdots\!50$$$$T^{12} +$$$$15\!\cdots\!00$$$$T^{14} +$$$$78\!\cdots\!25$$$$T^{16} +$$$$29\!\cdots\!50$$$$T^{18} +$$$$84\!\cdots\!25$$$$T^{20} )^{2}$$)
$7$ ($$( 1 - 823543 T^{2} )^{2}$$)($$( 1 + 751570 T^{2} + 678223072849 T^{4} )^{2}$$)($$( 1 - 4741522 T^{2} + 10982550245901 T^{4} - 16959553029024120120 T^{6} +$$$$19\!\cdots\!94$$$$T^{8} -$$$$18\!\cdots\!80$$$$T^{10} +$$$$13\!\cdots\!06$$$$T^{12} -$$$$78\!\cdots\!20$$$$T^{14} +$$$$34\!\cdots\!49$$$$T^{16} -$$$$10\!\cdots\!22$$$$T^{18} +$$$$14\!\cdots\!49$$$$T^{20} )^{2}$$)
$11$ ($$( 1 - 8814 T + 19487171 T^{2} )( 1 + 8814 T + 19487171 T^{2} )$$)($$( 1 - 35789342 T^{2} + 379749833583241 T^{4} )^{2}$$)($$( 1 - 64937722 T^{2} + 3455038618503141 T^{4} -$$$$11\!\cdots\!40$$$$T^{6} +$$$$33\!\cdots\!62$$$$T^{8} -$$$$69\!\cdots\!64$$$$T^{10} +$$$$12\!\cdots\!42$$$$T^{12} -$$$$16\!\cdots\!40$$$$T^{14} +$$$$18\!\cdots\!61$$$$T^{16} -$$$$13\!\cdots\!42$$$$T^{18} +$$$$78\!\cdots\!01$$$$T^{20} )^{2}$$)
$13$ ($$( 1 - 62748517 T^{2} )^{2}$$)($$( 1 - 22639370 T^{2} + 3937376385699289 T^{4} )^{2}$$)($$( 1 - 352407394 T^{2} + 62269551776806821 T^{4} -$$$$72\!\cdots\!68$$$$T^{6} +$$$$63\!\cdots\!46$$$$T^{8} -$$$$44\!\cdots\!72$$$$T^{10} +$$$$25\!\cdots\!94$$$$T^{12} -$$$$11\!\cdots\!28$$$$T^{14} +$$$$38\!\cdots\!49$$$$T^{16} -$$$$84\!\cdots\!54$$$$T^{18} +$$$$94\!\cdots\!49$$$$T^{20} )^{2}$$)
$17$ ($$( 1 - 22182 T + 410338673 T^{2} )( 1 + 22182 T + 410338673 T^{2} )$$)($$( 1 - 61393730 T^{2} + 168377826559400929 T^{4} )^{2}$$)($$( 1 - 2730456490 T^{2} + 3432956136635397261 T^{4} -$$$$26\!\cdots\!12$$$$T^{6} +$$$$15\!\cdots\!94$$$$T^{8} -$$$$68\!\cdots\!00$$$$T^{10} +$$$$25\!\cdots\!26$$$$T^{12} -$$$$76\!\cdots\!92$$$$T^{14} +$$$$16\!\cdots\!29$$$$T^{16} -$$$$21\!\cdots\!90$$$$T^{18} +$$$$13\!\cdots\!49$$$$T^{20} )^{2}$$)
$19$ ($$( 1 + 59722 T + 893871739 T^{2} )^{2}$$)($$( 1 - 11570 T + 893871739 T^{2} )^{4}$$)($$( 1 - 33436 T + 3303470211 T^{2} - 96285443658240 T^{3} + 5143998080498378646 T^{4} -$$$$12\!\cdots\!92$$$$T^{5} +$$$$45\!\cdots\!94$$$$T^{6} -$$$$76\!\cdots\!40$$$$T^{7} +$$$$23\!\cdots\!09$$$$T^{8} -$$$$21\!\cdots\!76$$$$T^{9} +$$$$57\!\cdots\!99$$$$T^{10} )^{4}$$)
$23$ ($$( 1 + 3404825447 T^{2} )^{2}$$)($$( 1 + 3725533390 T^{2} + 11592836324538749809 T^{4} )^{2}$$)($$( 1 + 14309806406 T^{2} + 96167780623641456861 T^{4} +$$$$42\!\cdots\!20$$$$T^{6} +$$$$14\!\cdots\!66$$$$T^{8} +$$$$48\!\cdots\!52$$$$T^{10} +$$$$17\!\cdots\!94$$$$T^{12} +$$$$57\!\cdots\!20$$$$T^{14} +$$$$14\!\cdots\!69$$$$T^{16} +$$$$25\!\cdots\!66$$$$T^{18} +$$$$20\!\cdots\!49$$$$T^{20} )^{2}$$)
$29$ ($$( 1 + 17249876309 T^{2} )^{2}$$)($$( 1 + 31499935018 T^{2} +$$$$29\!\cdots\!81$$$$T^{4} )^{2}$$)($$( 1 + 73882100390 T^{2} +$$$$28\!\cdots\!49$$$$T^{4} +$$$$79\!\cdots\!96$$$$T^{6} +$$$$17\!\cdots\!74$$$$T^{8} +$$$$33\!\cdots\!40$$$$T^{10} +$$$$53\!\cdots\!94$$$$T^{12} +$$$$70\!\cdots\!56$$$$T^{14} +$$$$74\!\cdots\!09$$$$T^{16} +$$$$57\!\cdots\!90$$$$T^{18} +$$$$23\!\cdots\!01$$$$T^{20} )^{2}$$)
$31$ ($$( 1 - 27512614111 T^{2} )^{2}$$)($$( 1 - 49885402622 T^{2} +$$$$75\!\cdots\!21$$$$T^{4} )^{2}$$)($$( 1 - 102708614914 T^{2} +$$$$77\!\cdots\!29$$$$T^{4} -$$$$38\!\cdots\!20$$$$T^{6} +$$$$15\!\cdots\!74$$$$T^{8} -$$$$46\!\cdots\!60$$$$T^{10} +$$$$11\!\cdots\!54$$$$T^{12} -$$$$21\!\cdots\!20$$$$T^{14} +$$$$33\!\cdots\!69$$$$T^{16} -$$$$33\!\cdots\!34$$$$T^{18} +$$$$24\!\cdots\!01$$$$T^{20} )^{2}$$)
$37$ ($$( 1 - 94931877133 T^{2} )^{2}$$)($$( 1 - 109874639450 T^{2} +$$$$90\!\cdots\!89$$$$T^{4} )^{2}$$)($$( 1 - 483705831538 T^{2} +$$$$12\!\cdots\!41$$$$T^{4} -$$$$20\!\cdots\!60$$$$T^{6} +$$$$27\!\cdots\!66$$$$T^{8} -$$$$29\!\cdots\!00$$$$T^{10} +$$$$24\!\cdots\!74$$$$T^{12} -$$$$16\!\cdots\!60$$$$T^{14} +$$$$88\!\cdots\!29$$$$T^{16} -$$$$31\!\cdots\!58$$$$T^{18} +$$$$59\!\cdots\!49$$$$T^{20} )^{2}$$)
$41$ ($$( 1 - 236886 T + 194754273881 T^{2} )( 1 + 236886 T + 194754273881 T^{2} )$$)($$( 1 - 226584602162 T^{2} +$$$$37\!\cdots\!61$$$$T^{4} )^{2}$$)($$( 1 - 1090625824570 T^{2} +$$$$56\!\cdots\!21$$$$T^{4} -$$$$19\!\cdots\!36$$$$T^{6} +$$$$47\!\cdots\!34$$$$T^{8} -$$$$98\!\cdots\!00$$$$T^{10} +$$$$18\!\cdots\!74$$$$T^{12} -$$$$27\!\cdots\!56$$$$T^{14} +$$$$31\!\cdots\!01$$$$T^{16} -$$$$22\!\cdots\!70$$$$T^{18} +$$$$78\!\cdots\!01$$$$T^{20} )^{2}$$)
$43$ ($$( 1 + 220510 T + 271818611107 T^{2} )^{2}$$)($$( 1 - 495062 T + 271818611107 T^{2} )^{4}$$)($$( 1 + 573020 T + 765614977707 T^{2} + 388334673397088640 T^{3} +$$$$29\!\cdots\!86$$$$T^{4} +$$$$14\!\cdots\!20$$$$T^{5} +$$$$80\!\cdots\!02$$$$T^{6} +$$$$28\!\cdots\!60$$$$T^{7} +$$$$15\!\cdots\!01$$$$T^{8} +$$$$31\!\cdots\!20$$$$T^{9} +$$$$14\!\cdots\!07$$$$T^{10} )^{4}$$)
$47$ ($$( 1 + 506623120463 T^{2} )^{2}$$)($$( 1 - 277104744290 T^{2} +$$$$25\!\cdots\!69$$$$T^{4} )^{2}$$)($$( 1 + 2220997832726 T^{2} +$$$$28\!\cdots\!69$$$$T^{4} +$$$$26\!\cdots\!20$$$$T^{6} +$$$$19\!\cdots\!22$$$$T^{8} +$$$$10\!\cdots\!72$$$$T^{10} +$$$$49\!\cdots\!18$$$$T^{12} +$$$$17\!\cdots\!20$$$$T^{14} +$$$$48\!\cdots\!21$$$$T^{16} +$$$$96\!\cdots\!46$$$$T^{18} +$$$$11\!\cdots\!49$$$$T^{20} )^{2}$$)
$53$ ($$( 1 + 1174711139837 T^{2} )^{2}$$)($$( 1 + 2021761791610 T^{2} +$$$$13\!\cdots\!69$$$$T^{4} )^{2}$$)($$( 1 + 3461178859478 T^{2} +$$$$63\!\cdots\!13$$$$T^{4} +$$$$75\!\cdots\!12$$$$T^{6} +$$$$64\!\cdots\!46$$$$T^{8} +$$$$53\!\cdots\!64$$$$T^{10} +$$$$88\!\cdots\!74$$$$T^{12} +$$$$14\!\cdots\!32$$$$T^{14} +$$$$16\!\cdots\!17$$$$T^{16} +$$$$12\!\cdots\!38$$$$T^{18} +$$$$50\!\cdots\!49$$$$T^{20} )^{2}$$)
$59$ ($$( 1 - 1030926 T + 2488651484819 T^{2} )( 1 + 1030926 T + 2488651484819 T^{2} )$$)($$( 1 - 2902252328702 T^{2} +$$$$61\!\cdots\!61$$$$T^{4} )^{2}$$)($$( 1 - 19732197121882 T^{2} +$$$$18\!\cdots\!29$$$$T^{4} -$$$$10\!\cdots\!80$$$$T^{6} +$$$$43\!\cdots\!06$$$$T^{8} -$$$$12\!\cdots\!44$$$$T^{10} +$$$$26\!\cdots\!66$$$$T^{12} -$$$$41\!\cdots\!80$$$$T^{14} +$$$$43\!\cdots\!49$$$$T^{16} -$$$$29\!\cdots\!62$$$$T^{18} +$$$$91\!\cdots\!01$$$$T^{20} )^{2}$$)
$61$ ($$( 1 - 3142742836021 T^{2} )^{2}$$)($$( 1 - 3094549289642 T^{2} +$$$$98\!\cdots\!41$$$$T^{4} )^{2}$$)($$( 1 - 8130200545282 T^{2} +$$$$45\!\cdots\!25$$$$T^{4} -$$$$16\!\cdots\!48$$$$T^{6} +$$$$61\!\cdots\!70$$$$T^{8} -$$$$19\!\cdots\!52$$$$T^{10} +$$$$60\!\cdots\!70$$$$T^{12} -$$$$16\!\cdots\!88$$$$T^{14} +$$$$43\!\cdots\!25$$$$T^{16} -$$$$77\!\cdots\!02$$$$T^{18} +$$$$93\!\cdots\!01$$$$T^{20} )^{2}$$)
$67$ ($$( 1 + 3851302 T + 6060711605323 T^{2} )^{2}$$)($$( 1 - 1400126 T + 6060711605323 T^{2} )^{4}$$)($$( 1 - 913660 T + 20744505994131 T^{2} - 20152579863740122560 T^{3} +$$$$20\!\cdots\!10$$$$T^{4} -$$$$17\!\cdots\!20$$$$T^{5} +$$$$12\!\cdots\!30$$$$T^{6} -$$$$74\!\cdots\!40$$$$T^{7} +$$$$46\!\cdots\!77$$$$T^{8} -$$$$12\!\cdots\!60$$$$T^{9} +$$$$81\!\cdots\!43$$$$T^{10} )^{4}$$)
$71$ ($$( 1 + 9095120158391 T^{2} )^{2}$$)($$( 1 + 5449089705838 T^{2} +$$$$82\!\cdots\!81$$$$T^{4} )^{2}$$)($$( 1 + 78176481465446 T^{2} +$$$$28\!\cdots\!33$$$$T^{4} +$$$$63\!\cdots\!56$$$$T^{6} +$$$$95\!\cdots\!42$$$$T^{8} +$$$$10\!\cdots\!48$$$$T^{10} +$$$$78\!\cdots\!02$$$$T^{12} +$$$$43\!\cdots\!16$$$$T^{14} +$$$$16\!\cdots\!53$$$$T^{16} +$$$$36\!\cdots\!66$$$$T^{18} +$$$$38\!\cdots\!01$$$$T^{20} )^{2}$$)
$73$ ($$( 1 + 4865614 T + 11047398519097 T^{2} )^{2}$$)($$( 1 + 2223598 T + 11047398519097 T^{2} )^{4}$$)($$( 1 - 4973170 T + 56350864331589 T^{2} -$$$$20\!\cdots\!80$$$$T^{3} +$$$$12\!\cdots\!10$$$$T^{4} -$$$$33\!\cdots\!20$$$$T^{5} +$$$$13\!\cdots\!70$$$$T^{6} -$$$$25\!\cdots\!20$$$$T^{7} +$$$$75\!\cdots\!97$$$$T^{8} -$$$$74\!\cdots\!70$$$$T^{9} +$$$$16\!\cdots\!57$$$$T^{10} )^{4}$$)
$79$ ($$( 1 - 19203908986159 T^{2} )^{2}$$)($$( 1 - 7153320805022 T^{2} +$$$$36\!\cdots\!81$$$$T^{4} )^{2}$$)($$( 1 - 126095156012386 T^{2} +$$$$68\!\cdots\!69$$$$T^{4} -$$$$20\!\cdots\!20$$$$T^{6} +$$$$42\!\cdots\!54$$$$T^{8} -$$$$77\!\cdots\!60$$$$T^{10} +$$$$15\!\cdots\!74$$$$T^{12} -$$$$28\!\cdots\!20$$$$T^{14} +$$$$34\!\cdots\!29$$$$T^{16} -$$$$23\!\cdots\!06$$$$T^{18} +$$$$68\!\cdots\!01$$$$T^{20} )^{2}$$)
$83$ ($$( 1 - 4808934 T + 27136050989627 T^{2} )( 1 + 4808934 T + 27136050989627 T^{2} )$$)($$( 1 - 45191963757710 T^{2} +$$$$73\!\cdots\!29$$$$T^{4} )^{2}$$)($$( 1 - 179430499509514 T^{2} +$$$$15\!\cdots\!93$$$$T^{4} -$$$$80\!\cdots\!80$$$$T^{6} +$$$$31\!\cdots\!46$$$$T^{8} -$$$$93\!\cdots\!16$$$$T^{10} +$$$$22\!\cdots\!34$$$$T^{12} -$$$$43\!\cdots\!80$$$$T^{14} +$$$$60\!\cdots\!77$$$$T^{16} -$$$$52\!\cdots\!34$$$$T^{18} +$$$$21\!\cdots\!49$$$$T^{20} )^{2}$$)
$89$ ($$( 1 - 7073118 T + 44231334895529 T^{2} )( 1 + 7073118 T + 44231334895529 T^{2} )$$)($$( 1 - 54294758858162 T^{2} +$$$$19\!\cdots\!41$$$$T^{4} )^{2}$$)($$( 1 - 287003084492698 T^{2} +$$$$42\!\cdots\!01$$$$T^{4} -$$$$40\!\cdots\!00$$$$T^{6} +$$$$27\!\cdots\!22$$$$T^{8} -$$$$13\!\cdots\!76$$$$T^{10} +$$$$53\!\cdots\!02$$$$T^{12} -$$$$15\!\cdots\!00$$$$T^{14} +$$$$31\!\cdots\!21$$$$T^{16} -$$$$42\!\cdots\!78$$$$T^{18} +$$$$28\!\cdots\!01$$$$T^{20} )^{2}$$)
$97$ ($$( 1 + 9938890 T + 80798284478113 T^{2} )^{2}$$)($$( 1 - 6867926 T + 80798284478113 T^{2} )^{4}$$)($$( 1 - 1390450 T + 285922062427293 T^{2} +$$$$26\!\cdots\!80$$$$T^{3} +$$$$35\!\cdots\!78$$$$T^{4} +$$$$61\!\cdots\!00$$$$T^{5} +$$$$28\!\cdots\!14$$$$T^{6} +$$$$17\!\cdots\!20$$$$T^{7} +$$$$15\!\cdots\!21$$$$T^{8} -$$$$59\!\cdots\!50$$$$T^{9} +$$$$34\!\cdots\!93$$$$T^{10} )^{4}$$)