Properties

Label 2.42
Level 2
Weight 42
Dimension 3
Nonzero newspaces 1
Newforms 2
Sturm bound 10
Trace bound 0

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 42 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{42}(\Gamma_1(2))\).

Total New Old
Modular forms 11 3 8
Cusp forms 9 3 6
Eisenstein series 2 0 2

Trace form

\(3q \) \(\mathstrut +\mathstrut 1048576q^{2} \) \(\mathstrut +\mathstrut 13906864044q^{3} \) \(\mathstrut +\mathstrut 3298534883328q^{4} \) \(\mathstrut +\mathstrut 49094989194930q^{5} \) \(\mathstrut +\mathstrut 4005383123238912q^{6} \) \(\mathstrut +\mathstrut 97714356676438488q^{7} \) \(\mathstrut +\mathstrut 1152921504606846976q^{8} \) \(\mathstrut +\mathstrut 30936992086866501639q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 1048576q^{2} \) \(\mathstrut +\mathstrut 13906864044q^{3} \) \(\mathstrut +\mathstrut 3298534883328q^{4} \) \(\mathstrut +\mathstrut 49094989194930q^{5} \) \(\mathstrut +\mathstrut 4005383123238912q^{6} \) \(\mathstrut +\mathstrut 97714356676438488q^{7} \) \(\mathstrut +\mathstrut 1152921504606846976q^{8} \) \(\mathstrut +\mathstrut 30936992086866501639q^{9} \) \(\mathstrut +\mathstrut 153200497216695828480q^{10} \) \(\mathstrut +\mathstrut 3264403333766748924036q^{11} \) \(\mathstrut +\mathstrut 15290758722277966086144q^{12} \) \(\mathstrut +\mathstrut 161882807152022753465994q^{13} \) \(\mathstrut +\mathstrut 352845035543974457114624q^{14} \) \(\mathstrut -\mathstrut 3539918996489522338057080q^{15} \) \(\mathstrut +\mathstrut 3626777458843887524118528q^{16} \) \(\mathstrut -\mathstrut 37011726883142944282175562q^{17} \) \(\mathstrut +\mathstrut 55583825877405288820113408q^{18} \) \(\mathstrut +\mathstrut 274230100811445606374810460q^{19} \) \(\mathstrut +\mathstrut 53980511485362616066375680q^{20} \) \(\mathstrut +\mathstrut 2665691359852998167875660896q^{21} \) \(\mathstrut -\mathstrut 3191041552072698539506925568q^{22} \) \(\mathstrut +\mathstrut 1420347666919737243157853064q^{23} \) \(\mathstrut +\mathstrut 4403965317698934946463219712q^{24} \) \(\mathstrut +\mathstrut 54412888097875513082262174525q^{25} \) \(\mathstrut +\mathstrut 193675559200226950852527521792q^{26} \) \(\mathstrut +\mathstrut 293544196044657269619833966520q^{27} \) \(\mathstrut +\mathstrut 107438071366395535287216242688q^{28} \) \(\mathstrut -\mathstrut 1238427538159622404128372563910q^{29} \) \(\mathstrut -\mathstrut 3198844223373791442948618977280q^{30} \) \(\mathstrut -\mathstrut 565073962679875259305481759904q^{31} \) \(\mathstrut +\mathstrut 1267650600228229401496703205376q^{32} \) \(\mathstrut +\mathstrut 2233551046463051372662468702608q^{33} \) \(\mathstrut +\mathstrut 17234179508571566375244140642304q^{34} \) \(\mathstrut -\mathstrut 97248489612709189284759665330160q^{35} \) \(\mathstrut +\mathstrut 34015582527923818408303461924864q^{36} \) \(\mathstrut -\mathstrut 101592630862331863544766032309742q^{37} \) \(\mathstrut +\mathstrut 144996736400908851639068697559040q^{38} \) \(\mathstrut +\mathstrut 640160633638918340067446036904168q^{39} \) \(\mathstrut +\mathstrut 168445728070821787776313699860480q^{40} \) \(\mathstrut +\mathstrut 768192138006768072331689412248126q^{41} \) \(\mathstrut +\mathstrut 4057996358704299679930133010972672q^{42} \) \(\mathstrut -\mathstrut 9163911628959853913209536056311836q^{43} \) \(\mathstrut +\mathstrut 3589249423227279134970318931623936q^{44} \) \(\mathstrut -\mathstrut 30457369032504081176750813707625910q^{45} \) \(\mathstrut +\mathstrut 29811534820383674194267711022825472q^{46} \) \(\mathstrut -\mathstrut 12260960588935821767780288588908272q^{47} \) \(\mathstrut +\mathstrut 16812367012661916406114713279135744q^{48} \) \(\mathstrut -\mathstrut 25596406892660163029921184065783829q^{49} \) \(\mathstrut +\mathstrut 147489600972651489691044136380006400q^{50} \) \(\mathstrut -\mathstrut 182678347564418655807945350847940584q^{51} \) \(\mathstrut +\mathstrut 177992028800668832354384608801849344q^{52} \) \(\mathstrut -\mathstrut 625375082980902027370788377449928766q^{53} \) \(\mathstrut +\mathstrut 810306378590012747923651603590021120q^{54} \) \(\mathstrut +\mathstrut 550426134204771570148170929066219160q^{55} \) \(\mathstrut +\mathstrut 387957219383635932970666138454196224q^{56} \) \(\mathstrut -\mathstrut 442953519980269300084782666393665040q^{57} \) \(\mathstrut -\mathstrut 1585298523526682507321181181449338880q^{58} \) \(\mathstrut +\mathstrut 177563983295764361517342239221260180q^{59} \) \(\mathstrut -\mathstrut 3892182098025379135645853384001454080q^{60} \) \(\mathstrut -\mathstrut 5463201135704660666208213208341875814q^{61} \) \(\mathstrut -\mathstrut 7012792278966542721658673238982524928q^{62} \) \(\mathstrut +\mathstrut 26310155382295499484506243647288915704q^{63} \) \(\mathstrut +\mathstrut 3987683987354747618711421180841033728q^{64} \) \(\mathstrut +\mathstrut 12473259455640304370441775300271028220q^{65} \) \(\mathstrut -\mathstrut 31015853645488527189477610831170502656q^{66} \) \(\mathstrut +\mathstrut 71683283838926171050853516149998220908q^{67} \) \(\mathstrut -\mathstrut 40694824072085237602584124037227610112q^{68} \) \(\mathstrut -\mathstrut 11480840010959325121257435993672114912q^{69} \) \(\mathstrut -\mathstrut 114117111792639301686346513623086530560q^{70} \) \(\mathstrut +\mathstrut 68110973123647230466528954560382296216q^{71} \) \(\mathstrut +\mathstrut 61115062868483640529874307679002820608q^{72} \) \(\mathstrut -\mathstrut 294908420905755625150102017496226933346q^{73} \) \(\mathstrut +\mathstrut 358933845813325666940616726553416433664q^{74} \) \(\mathstrut -\mathstrut 149075468778282886564381918940741001900q^{75} \) \(\mathstrut +\mathstrut 301519184528369137116851211238071336960q^{76} \) \(\mathstrut -\mathstrut 796259039077942095596584187532209589984q^{77} \) \(\mathstrut +\mathstrut 791944053109205052642588176234877812736q^{78} \) \(\mathstrut -\mathstrut 1467129308592083502686260888480869532560q^{79} \) \(\mathstrut +\mathstrut 59352200051452113588758453977538887680q^{80} \) \(\mathstrut +\mathstrut 1825606948109165162789233850315793931563q^{81} \) \(\mathstrut +\mathstrut 1858246690007324705570778546446744420352q^{82} \) \(\mathstrut +\mathstrut 665984279782956439537682608316709433884q^{83} \) \(\mathstrut +\mathstrut 2930958646220388991634913623732750647296q^{84} \) \(\mathstrut +\mathstrut 907701952915589923696197022820240971140q^{85} \) \(\mathstrut -\mathstrut 3069134989805620595871083685892449107968q^{86} \) \(\mathstrut -\mathstrut 17068192400013102750887440771225829791320q^{87} \) \(\mathstrut -\mathstrut 3508587291220306237862197575696953376768q^{88} \) \(\mathstrut +\mathstrut 14607841393604595000567679910075985192270q^{89} \) \(\mathstrut -\mathstrut 33059449148344087288488905373318654197760q^{90} \) \(\mathstrut +\mathstrut 18031837917819409202012303003569888867536q^{91} \) \(\mathstrut +\mathstrut 1561688775262764164166701740916069105664q^{92} \) \(\mathstrut +\mathstrut 55858944591888014581432169202537944899968q^{93} \) \(\mathstrut -\mathstrut 40445670686694062392590229249526392160256q^{94} \) \(\mathstrut +\mathstrut 90543084377116752054454370649641547666600q^{95} \) \(\mathstrut +\mathstrut 4842211075132204945687306119655049920512q^{96} \) \(\mathstrut -\mathstrut 95565478890036662057547911249774079434202q^{97} \) \(\mathstrut +\mathstrut 36731367279780021226536126103678601920512q^{98} \) \(\mathstrut -\mathstrut 158014553036426914776149850133844786493132q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{42}^{\mathrm{new}}(\Gamma_1(2))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2.42.a \(\chi_{2}(1, \cdot)\) 2.42.a.a 1 1
2.42.a.b 2

Decomposition of \(S_{42}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{42}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{42}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)