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Properties

Label 16.42
Level 16
Weight 42
Dimension 182
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 672
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 42 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(672\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{42}(\Gamma_1(16))\).

Total New Old
Modular forms 335 187 148
Cusp forms 321 182 139
Eisenstein series 14 5 9

Trace form

\( 182 q - 2 q^{2} - 3486784402 q^{3} - 3249459927384 q^{4} + 105262218614518 q^{5} - 12174338461858448 q^{6} + 283370945575456480 q^{7} + 3779902660176068404 q^{8} + 236216753458921118596 q^{9} + O(q^{10}) \) \( 182 q - 2 q^{2} - 3486784402 q^{3} - 3249459927384 q^{4} + 105262218614518 q^{5} - 12174338461858448 q^{6} + 283370945575456480 q^{7} + 3779902660176068404 q^{8} + 236216753458921118596 q^{9} - 513582184411548895156 q^{10} - 1187834668176930690670 q^{11} - 32338458524284205174204 q^{12} - 29277446168674600343402 q^{13} - 108034257086206623482788 q^{14} + 5578579652081758925770404 q^{15} + 4508411571251494461874072 q^{16} - 1433213107248184658073244 q^{17} + 205963723883451590667869502 q^{18} + 441130753018403063133725110 q^{19} - 519944332036353139106440868 q^{20} - 1047982344360985473721909436 q^{21} + 9426084430851608386572796420 q^{22} - 4561960260066985113082055520 q^{23} - 19131932859471475759248510800 q^{24} + 145615952031116507499277436652 q^{25} + 443259533458912266047697575944 q^{26} + 116653146269407703307994349912 q^{27} - 358765392591854515438258186792 q^{28} + 716600386696018810364807142558 q^{29} - 1788817859164397467984966656684 q^{30} - 961975207144178639413252507280 q^{31} + 22424825442059597071478453486408 q^{32} - 5081645223660258304623411949124 q^{33} + 122447315354304473329839461954484 q^{34} - 80257178571833018403935882789188 q^{35} - 46719501647179700951390592093332 q^{36} + 32958592952945531246848296831806 q^{37} - 557348711416519344182121628797312 q^{38} - 411329780923622130679410390845408 q^{39} - 3963268796108579066632703193365368 q^{40} + 387304146369101802205580048105544 q^{41} + 3868947464807742056277673728935800 q^{42} + 13406861841786848662865297732820890 q^{43} - 8987907866557563728849796713715196 q^{44} - 539025719853036409218721662746982 q^{45} - 6392118850972912915810034189460276 q^{46} + 39188426060048846075153133399912016 q^{47} - 53062529615281150286579636623290392 q^{48} - 835632559828432267778579703551799206 q^{49} + 283505956417046854963150093754289030 q^{50} + 135455614513075437537227109206677604 q^{51} - 101742099733909036682793603621983244 q^{52} - 472110765756401346567228995765976850 q^{53} - 964818053066259109787644053477369056 q^{54} - 410462252503858630312619364775158304 q^{55} - 2327037056706424845688030800804237416 q^{56} + 1028044164553833490084922102021677120 q^{57} - 3404926189835221209165725184434273832 q^{58} + 4130644417930838517961641992300344650 q^{59} + 23270237228383062432318697875014247552 q^{60} - 11671291864104169978488035284950851386 q^{61} + 38291494163329528804107265082342990896 q^{62} - 5569173359356012894230802479231602076 q^{63} + 49605319014376564503724133837636701824 q^{64} - 22004904609936671670437919274216482860 q^{65} + 38778223306186304465441250307495869364 q^{66} - 40714378947899944354088138454023473690 q^{67} + 41864239358797741607114144963070532560 q^{68} + 98842333345341316857806761411367166132 q^{69} - 226847955885731256180747891621126167680 q^{70} + 95662757309967009751576979529396999648 q^{71} + 102563752340482617203177659839771714084 q^{72} - 28263740444780166367706454890678036280 q^{73} + 53958874052473183529926360162638520524 q^{74} - 2166877707262037621310650878180488474282 q^{75} + 744894860745204546250856642739145786260 q^{76} - 878919628450785400416377374802320854716 q^{77} + 1436000096656275071009390786078188833116 q^{78} + 4988198351961137783808752472725935758272 q^{79} - 1670026870043058549150638678315012516056 q^{80} - 18334590213947257747883730402337340276898 q^{81} - 2616538637671147434038672431823298002400 q^{82} - 12556121595030331967303854748512028406482 q^{83} + 5305062042233236531658036174253081156520 q^{84} - 2315731703536583713244752928975528806604 q^{85} + 9753218773306229798333945136361382377860 q^{86} + 28683205592542066658588525586728910423840 q^{87} + 1738829817472308374640245738020125410808 q^{88} - 7098815675166096007728437667893801538552 q^{89} + 38931060102499274118025191637328327100312 q^{90} - 27231883869887330461907250017934035408316 q^{91} - 63416203870005698500440359933711869032264 q^{92} - 14775568642879727386834682875873509660784 q^{93} - 76092818172220170962481092293603126966000 q^{94} - 58182308588303268863750273594282107789548 q^{95} - 10586814369625449977970489169282143296848 q^{96} - 6962981559017306802283608171691329490524 q^{97} - 27179627901618418184738210634586101657126 q^{98} - 48298191424883669661020563658569787439986 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{42}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.42.a \(\chi_{16}(1, \cdot)\) 16.42.a.a 1 1
16.42.a.b 2
16.42.a.c 3
16.42.a.d 4
16.42.a.e 5
16.42.a.f 5
16.42.b \(\chi_{16}(9, \cdot)\) None 0 1
16.42.e \(\chi_{16}(5, \cdot)\) 16.42.e.a 162 2

Decomposition of \(S_{42}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{42}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{42}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{42}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{42}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{42}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)