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Properties

Label 16.24
Level 16
Weight 24
Dimension 101
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 384
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 24 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(384\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_1(16))\).

Total New Old
Modular forms 191 106 85
Cusp forms 177 101 76
Eisenstein series 14 5 9

Trace form

\( 101 q - 2 q^{2} + 177146 q^{3} - 10051000 q^{4} + 17776696 q^{5} - 34901168 q^{6} + 1949733464 q^{7} + 30640123156 q^{8} + 311299352311 q^{9} + O(q^{10}) \) \( 101 q - 2 q^{2} + 177146 q^{3} - 10051000 q^{4} + 17776696 q^{5} - 34901168 q^{6} + 1949733464 q^{7} + 30640123156 q^{8} + 311299352311 q^{9} - 588557473108 q^{10} + 2319296411846 q^{11} - 10365979822556 q^{12} + 2642407039520 q^{13} - 12080734219780 q^{14} - 26021252276532 q^{15} - 289040624328680 q^{16} - 71179668690718 q^{17} - 26224757044386 q^{18} + 384411871927378 q^{19} + 975591457739644 q^{20} - 488611228948364 q^{21} + 10343003441864132 q^{22} - 5818970285179512 q^{23} + 34611890767026352 q^{24} + 20411609150781629 q^{25} - 21327501111981944 q^{26} - 755508492371632 q^{27} + 46280415333947032 q^{28} + 10001424757921800 q^{29} + 377447059085653236 q^{30} - 27458785011159344 q^{31} + 665341822589933768 q^{32} - 437922770794372340 q^{33} + 2432831325765866996 q^{34} + 409887694814637164 q^{35} - 4470185640940367060 q^{36} + 90546641694748080 q^{37} + 6581420100979340448 q^{38} + 2103652896914624872 q^{39} + 11729059863434267464 q^{40} + 2097811779257112414 q^{41} - 25626558302504154440 q^{42} - 19807859747829588978 q^{43} + 56330410988545478564 q^{44} - 5288860217568517404 q^{45} - 25656422055555001172 q^{46} - 19937501875662676640 q^{47} - 18417550651824359192 q^{48} - 295820720234912121487 q^{49} + 55823835350313630726 q^{50} - 134241607525055558500 q^{51} - 95033251348091456556 q^{52} + 61839604740688788176 q^{53} - 79625461088775592928 q^{54} - 131177525254463064168 q^{55} - 174568938178308505832 q^{56} + 105086166253981385200 q^{57} + 704211462540533577368 q^{58} + 898407537940793041326 q^{59} - 1882935325401102280512 q^{60} - 584825566147856530464 q^{61} - 484915175234762488784 q^{62} + 1955812443848043341436 q^{63} - 645670895962104682240 q^{64} + 1378716349737152735824 q^{65} - 4773503780018349045548 q^{66} + 453849429312059155346 q^{67} + 2880641598187038235920 q^{68} - 728966103032535482748 q^{69} - 5201366682987420471680 q^{70} + 3117697388767923831576 q^{71} - 8923334146106834012028 q^{72} + 2873112734549390847742 q^{73} + 3784165403352193353516 q^{74} - 8630401216653136223238 q^{75} + 974258335374810902516 q^{76} - 7892904682151627577740 q^{77} + 3520740256949405895356 q^{78} + 3952202818332456266544 q^{79} - 31824135621398137002328 q^{80} - 75033271034859430569003 q^{81} + 8106598016519235500800 q^{82} - 4708719279196830255254 q^{83} + 20271006091160349119656 q^{84} - 16695222600928269068632 q^{85} + 56161332247142875751364 q^{86} - 14060896771764706007640 q^{87} - 41178571396980762509832 q^{88} + 25770260157052733876430 q^{89} + 203080837481548563191256 q^{90} + 56786127397874544872724 q^{91} - 219664490535386633679624 q^{92} - 23151768815947900966480 q^{93} + 230485625193146216808784 q^{94} + 377515582905313826521308 q^{95} + 401339582662066662760112 q^{96} - 52068968829279618175758 q^{97} - 665310425633387965377414 q^{98} - 4777043757817109779454 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_1(16))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
16.24.a \(\chi_{16}(1, \cdot)\) 16.24.a.a 1 1
16.24.a.b 2
16.24.a.c 2
16.24.a.d 3
16.24.a.e 3
16.24.b \(\chi_{16}(9, \cdot)\) None 0 1
16.24.e \(\chi_{16}(5, \cdot)\) 16.24.e.a 90 2

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)