Properties

Label 16.11
Level 16
Weight 11
Dimension 43
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 176
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16\( 16 = 2^{4} \) \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(176\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(16))\).

Total New Old
Modular forms 87 47 40
Cusp forms 73 43 30
Eisenstein series 14 4 10

Trace form

\( 43q - 2q^{2} - 2q^{3} - 1256q^{4} + 4672q^{5} - 17216q^{6} - 4q^{7} + 69124q^{8} - 130227q^{9} + O(q^{10}) \) \( 43q - 2q^{2} - 2q^{3} - 1256q^{4} + 4672q^{5} - 17216q^{6} - 4q^{7} + 69124q^{8} - 130227q^{9} - 147364q^{10} - 45906q^{11} - 10988q^{12} - 357936q^{13} + 757836q^{14} - 469032q^{16} - 2203162q^{17} + 2066926q^{18} - 5107042q^{19} + 5301516q^{20} - 5423444q^{21} - 20568924q^{22} - 8279748q^{23} + 58519728q^{24} + 30271831q^{25} - 18451512q^{26} - 25871552q^{27} - 36459784q^{28} - 30835296q^{29} + 132781252q^{30} - 52661752q^{32} + 33578492q^{33} + 68474900q^{34} + 14674460q^{35} - 15810676q^{36} - 249606160q^{37} + 156046000q^{38} - 279841732q^{39} - 125381720q^{40} + 379964826q^{41} + 107395416q^{42} + 172486862q^{43} + 73663988q^{44} - 1193615148q^{45} - 437620836q^{46} + 625190376q^{48} + 2211896295q^{49} - 875760314q^{50} - 72924900q^{51} - 771392444q^{52} - 532004304q^{53} + 913650464q^{54} - 1427102468q^{55} - 1385623464q^{56} + 3496598016q^{57} + 37561720q^{58} + 1543683854q^{59} + 318869600q^{60} - 1605958320q^{61} - 983062992q^{62} - 867678656q^{64} + 5467552032q^{65} + 768197860q^{66} - 4830427746q^{67} - 855827792q^{68} - 5413745972q^{69} - 5103882496q^{70} + 7572888316q^{71} + 6888513460q^{72} + 5245381658q^{73} + 2513658844q^{74} - 11656678318q^{75} - 2250244316q^{76} - 6423350036q^{77} + 14243324268q^{78} - 13115458328q^{80} - 6608616565q^{81} + 2724305648q^{82} + 16141605438q^{83} - 1633924184q^{84} - 4005542352q^{85} - 4025865500q^{86} - 31832612676q^{87} + 1023457912q^{88} - 2520582342q^{89} + 18960485240q^{90} + 19874217404q^{91} + 28060187160q^{92} + 15789813088q^{93} - 14829002256q^{94} + 23525947312q^{96} - 16976779898q^{97} - 43134832310q^{98} - 25616384098q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(16))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
16.11.c \(\chi_{16}(15, \cdot)\) 16.11.c.a 1 1
16.11.c.b 4
16.11.d \(\chi_{16}(7, \cdot)\) None 0 1
16.11.f \(\chi_{16}(3, \cdot)\) 16.11.f.a 38 2

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( ( 1 - 243 T )( 1 + 243 T ) \))(\( 1 - 23460 T^{2} + 3462362982 T^{4} - 81799962047460 T^{6} + 12157665459056928801 T^{8} \))
$5$ (\( 1 - 474 T + 9765625 T^{2} \))(\( ( 1 - 2100 T + 2017430 T^{2} - 20507812500 T^{3} + 95367431640625 T^{4} )^{2} \))
$7$ (\( ( 1 - 16807 T )( 1 + 16807 T ) \))(\( 1 - 1005064132 T^{2} + 411300244861899078 T^{4} - \)\(80\!\cdots\!32\)\( T^{6} + \)\(63\!\cdots\!01\)\( T^{8} \))
$11$ (\( ( 1 - 161051 T )( 1 + 161051 T ) \))(\( 1 - 19840803940 T^{2} + \)\(44\!\cdots\!82\)\( T^{4} - \)\(13\!\cdots\!40\)\( T^{6} + \)\(45\!\cdots\!01\)\( T^{8} \))
$13$ (\( 1 - 683050 T + 137858491849 T^{2} \))(\( ( 1 + 520492 T + 254812664694 T^{2} + 71754242139469708 T^{3} + \)\(19\!\cdots\!01\)\( T^{4} )^{2} \))
$17$ (\( 1 - 2186850 T + 2015993900449 T^{2} \))(\( ( 1 + 2195004 T + 5145278472902 T^{2} + 4425114675461156796 T^{3} + \)\(40\!\cdots\!01\)\( T^{4} )^{2} \))
$19$ (\( ( 1 - 2476099 T )( 1 + 2476099 T ) \))(\( 1 - 3663898849060 T^{2} + \)\(45\!\cdots\!22\)\( T^{4} - \)\(13\!\cdots\!60\)\( T^{6} + \)\(14\!\cdots\!01\)\( T^{8} \))
$23$ (\( ( 1 - 6436343 T )( 1 + 6436343 T ) \))(\( 1 - 82119401461060 T^{2} + \)\(46\!\cdots\!82\)\( T^{4} - \)\(14\!\cdots\!60\)\( T^{6} + \)\(29\!\cdots\!01\)\( T^{8} \))
$29$ (\( 1 + 32319798 T + 420707233300201 T^{2} \))(\( ( 1 - 15568404 T + 902007355177526 T^{2} - \)\(65\!\cdots\!04\)\( T^{3} + \)\(17\!\cdots\!01\)\( T^{4} )^{2} \))
$31$ (\( ( 1 - 28629151 T )( 1 + 28629151 T ) \))(\( 1 - 1229395698322180 T^{2} + \)\(92\!\cdots\!02\)\( T^{4} - \)\(82\!\cdots\!80\)\( T^{6} + \)\(45\!\cdots\!01\)\( T^{8} \))
$37$ (\( 1 - 11178650 T + 4808584372417849 T^{2} \))(\( ( 1 + 83083340 T + 6979856299974678 T^{2} + \)\(39\!\cdots\!60\)\( T^{3} + \)\(23\!\cdots\!01\)\( T^{4} )^{2} \))
$41$ (\( 1 - 207190098 T + 13422659310152401 T^{2} \))(\( ( 1 - 86387364 T + 18423149137257446 T^{2} - \)\(11\!\cdots\!64\)\( T^{3} + \)\(18\!\cdots\!01\)\( T^{4} )^{2} \))
$43$ (\( ( 1 - 147008443 T )( 1 + 147008443 T ) \))(\( 1 + 888082514945180 T^{2} - \)\(50\!\cdots\!78\)\( T^{4} + \)\(41\!\cdots\!80\)\( T^{6} + \)\(21\!\cdots\!01\)\( T^{8} \))
$47$ (\( ( 1 - 229345007 T )( 1 + 229345007 T ) \))(\( 1 - 196091355038080132 T^{2} + \)\(15\!\cdots\!38\)\( T^{4} - \)\(54\!\cdots\!32\)\( T^{6} + \)\(76\!\cdots\!01\)\( T^{8} \))
$53$ (\( 1 + 783188550 T + 174887470365513049 T^{2} \))(\( ( 1 + 177944076 T + 213352476870696662 T^{2} + \)\(31\!\cdots\!24\)\( T^{3} + \)\(30\!\cdots\!01\)\( T^{4} )^{2} \))
$59$ (\( ( 1 - 714924299 T )( 1 + 714924299 T ) \))(\( 1 - 815549572994663140 T^{2} + \)\(68\!\cdots\!82\)\( T^{4} - \)\(21\!\cdots\!40\)\( T^{6} + \)\(68\!\cdots\!01\)\( T^{8} \))
$61$ (\( 1 + 1330090102 T + 713342911662882601 T^{2} \))(\( ( 1 + 974574188 T + 1661874172242478518 T^{2} + \)\(69\!\cdots\!88\)\( T^{3} + \)\(50\!\cdots\!01\)\( T^{4} )^{2} \))
$67$ (\( ( 1 - 1350125107 T )( 1 + 1350125107 T ) \))(\( 1 - 5292742361877207460 T^{2} + \)\(13\!\cdots\!82\)\( T^{4} - \)\(17\!\cdots\!60\)\( T^{6} + \)\(11\!\cdots\!01\)\( T^{8} \))
$71$ (\( ( 1 - 1804229351 T )( 1 + 1804229351 T ) \))(\( 1 - 11040185613269882308 T^{2} + \)\(50\!\cdots\!18\)\( T^{4} - \)\(11\!\cdots\!08\)\( T^{6} + \)\(11\!\cdots\!01\)\( T^{8} \))
$73$ (\( 1 - 3740362450 T + 4297625829703557649 T^{2} \))(\( ( 1 - 752509604 T + 7133539166909268582 T^{2} - \)\(32\!\cdots\!96\)\( T^{3} + \)\(18\!\cdots\!01\)\( T^{4} )^{2} \))
$79$ (\( ( 1 - 3077056399 T )( 1 + 3077056399 T ) \))(\( 1 + 5042168236353513596 T^{2} - \)\(12\!\cdots\!94\)\( T^{4} + \)\(45\!\cdots\!96\)\( T^{6} + \)\(80\!\cdots\!01\)\( T^{8} \))
$83$ (\( ( 1 - 3939040643 T )( 1 + 3939040643 T ) \))(\( 1 - 45281007302789483812 T^{2} + \)\(92\!\cdots\!58\)\( T^{4} - \)\(10\!\cdots\!12\)\( T^{6} + \)\(57\!\cdots\!01\)\( T^{8} \))
$89$ (\( 1 + 8562016398 T + 31181719929966183601 T^{2} \))(\( ( 1 - 3020717028 T + 27059817309971120678 T^{2} - \)\(94\!\cdots\!28\)\( T^{3} + \)\(97\!\cdots\!01\)\( T^{4} )^{2} \))
$97$ (\( 1 + 8684532350 T + 73742412689492826049 T^{2} \))(\( ( 1 + 4146123772 T + \)\(13\!\cdots\!94\)\( T^{2} + \)\(30\!\cdots\!28\)\( T^{3} + \)\(54\!\cdots\!01\)\( T^{4} )^{2} \))
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