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Properties

Label 3.32
Level 3
Weight 32
Dimension 5
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 21
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 32 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{32}(\Gamma_1(3))\).

Total New Old
Modular forms 11 5 6
Cusp forms 9 5 4
Eisenstein series 2 0 2

Trace form

\( 5 q - 47154 q^{2} - 14348907 q^{3} + 4017461156 q^{4} + 42691654830 q^{5} - 457758831114 q^{6} - 36219146721584 q^{7} - 202334457633000 q^{8} + 1029455660473245 q^{9} + O(q^{10}) \) \( 5 q - 47154 q^{2} - 14348907 q^{3} + 4017461156 q^{4} + 42691654830 q^{5} - 457758831114 q^{6} - 36219146721584 q^{7} - 202334457633000 q^{8} + 1029455660473245 q^{9} + 7843244819413140 q^{10} + 7416721527558828 q^{11} - 63424968526546956 q^{12} - 159873673123219538 q^{13} + 948152179120067328 q^{14} - 840167092935127890 q^{15} - 270289393420755184 q^{16} + 11428574064429502026 q^{17} - 9708590442791078946 q^{18} - 6307050634881659468 q^{19} + 387588068358666795480 q^{20} + 218697406028192789424 q^{21} + 1289832635986953576552 q^{22} - 3563793856502864210328 q^{23} + 1696082717180303039736 q^{24} - 421540450337265059725 q^{25} + 30900186892841149358580 q^{26} - 2954312706550833698643 q^{27} - 51535146418446512880512 q^{28} - 94015526311718203977786 q^{29} + 4116606088617801579780 q^{30} - 147965801759909551856504 q^{31} + 301166524766347461961056 q^{32} + 202999719348585157475916 q^{33} - 498265831452276101590308 q^{34} - 1034090636158405092612000 q^{35} + 827159625555117272954244 q^{36} + 1634456445324416225593606 q^{37} + 7229729356829652168672600 q^{38} - 337197606189342901165746 q^{39} - 7923131820770580343540080 q^{40} + 6082972355892352253197746 q^{41} - 21025057333231750442585472 q^{42} + 15609677808503818915135852 q^{43} - 12629504162683577657332560 q^{44} + 8789833143942689998004670 q^{45} + 10783892573227755589916016 q^{46} - 54339478357153758722156064 q^{47} - 99296374849559312450665392 q^{48} - 308884493794510231943391507 q^{49} + 724552303801336818670536450 q^{50} - 640235950201287165693950550 q^{51} + 61255757408146396331569816 q^{52} + 1937194937495493219157383342 q^{53} - 94248483964384696654108986 q^{54} - 1233554413651975262428987320 q^{55} + 3692971057494070674392559360 q^{56} - 2276503469597674147373598060 q^{57} - 10268475279806928918249245340 q^{58} + 9291126661253680568645111628 q^{59} - 9972032461013103660003207240 q^{60} + 457805438410064489129099182 q^{61} + 27786791375575028983290730512 q^{62} - 7457201122009124611139204016 q^{63} - 36379924672911095108455222720 q^{64} + 41500629474177367235163676020 q^{65} - 65437529128156556431649062200 q^{66} - 35706304616832398184271818284 q^{67} + 163393315458583590686939515848 q^{68} - 49599374156613537922732050072 q^{69} + 19406623784210672896689638400 q^{70} + 100222737978749051527848624600 q^{71} - 41658870543815164636505817000 q^{72} - 147159611271252233721349873118 q^{73} + 55765523139072090134755851588 q^{74} - 127977667014608618163125399325 q^{75} - 218320211258891332797326819888 q^{76} + 502024601283026332663468310592 q^{77} - 134368272546119256735378912924 q^{78} + 82900091158241303320067484760 q^{79} - 326542584927474230605375397280 q^{80} + 211955791376081017571472166005 q^{81} - 1006284659211487984847226386868 q^{82} - 884315070214333812928909526988 q^{83} + 1298238351262084546424823100032 q^{84} + 2644233596665313376577987155420 q^{85} - 3391767048943680982419672079512 q^{86} + 2132243728989136967843366600070 q^{87} + 5455782493331958671339366733600 q^{88} - 4258254695337838047651584076558 q^{89} + 1614854555164462249187114287860 q^{90} + 1164411861304536179232384640736 q^{91} - 10740520423523891226143579200224 q^{92} + 3059472014481751904231940546216 q^{93} + 587626729271457730504686595584 q^{94} - 11065014721929869255610757530120 q^{95} + 9135839246795500616300901376224 q^{96} + 14957014796617442855030173312906 q^{97} - 15313449381225718034672104137282 q^{98} + 1527037191739841569375211511372 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{32}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.32.a \(\chi_{3}(1, \cdot)\) 3.32.a.a 2 1
3.32.a.b 3

Decomposition of \(S_{32}^{\mathrm{old}}(\Gamma_1(3))\) into lower level spaces

\( S_{32}^{\mathrm{old}}(\Gamma_1(3)) \cong \) \(S_{32}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)