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Properties

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

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 42 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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

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