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Properties

Label 15.32
Level 15
Weight 32
Dimension 172
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 512
Trace bound 1

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 32 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(512\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{32}(\Gamma_1(15))\).

Total New Old
Modular forms 256 180 76
Cusp forms 240 172 68
Eisenstein series 16 8 8

Trace form

\( 172 q + 28772 q^{2} + 56888718 q^{3} - 14477373256 q^{4} - 5156469444 q^{5} - 896300417028 q^{6} + 14735399235448 q^{7} - 113154307334916 q^{8} - 2470693585135788 q^{9} + O(q^{10}) \) \( 172 q + 28772 q^{2} + 56888718 q^{3} - 14477373256 q^{4} - 5156469444 q^{5} - 896300417028 q^{6} + 14735399235448 q^{7} - 113154307334916 q^{8} - 2470693585135788 q^{9} - 14520896915645096 q^{10} + 20130239997851792 q^{11} - 27401538779556780 q^{12} - 502765201702642160 q^{13} + 1966622368340848968 q^{14} + 2857685393741060334 q^{15} - 67538235405161058192 q^{16} - 32307890079494756512 q^{17} + 34471643636932588548 q^{18} - 377994935961689536240 q^{19} + 355863315602269567084 q^{20} - 852364714367670148680 q^{21} - 2392433276461093630584 q^{22} + 5889494496509987212968 q^{23} - 9450452829833159358960 q^{24} + 35965227106752357949276 q^{25} - 70970429804830694383096 q^{26} + 73925839748298585454398 q^{27} - 222851519919462369893960 q^{28} + 108710546317629511861000 q^{29} - 468965955094032079638384 q^{30} + 181615519165297884579440 q^{31} - 1542591529690184320612076 q^{32} + 582814046901781992403896 q^{33} - 2431526601283260669596632 q^{34} + 2456135973322595926005640 q^{35} + 11412248162426446725164088 q^{36} - 6711708342836247306157712 q^{37} + 14863564233664865716302248 q^{38} - 11076990684759521585710092 q^{39} + 25563457829122622247546248 q^{40} - 7771116705780493002883880 q^{41} - 10335712900064995412132448 q^{42} + 43212055553629679582300488 q^{43} - 251600094845840541382061192 q^{44} + 66826645215351377185192356 q^{45} - 286388479705333090570234360 q^{46} - 158274198874136603942826280 q^{47} + 40505701819423486347127284 q^{48} - 539195556497704736788617436 q^{49} + 500403281295898340615658524 q^{50} + 1371103184073930320583842316 q^{51} + 715563139769188086444786832 q^{52} - 1445926275423714285404081152 q^{53} - 198730707144261481240317324 q^{54} - 1220362640338653171802550544 q^{55} - 27317135368190779241812800 q^{56} + 6193874601050184328289042376 q^{57} - 1618854934163433983111664264 q^{58} + 2925609710728834314064630400 q^{59} - 30460281514396056298189856904 q^{60} + 15144563388619381285130078936 q^{61} - 35449825522271493812932136472 q^{62} + 21160086597087718931339491224 q^{63} + 31899077577576871647808740424 q^{64} - 61805767802849712738040779232 q^{65} + 108880469201836613049562300992 q^{66} + 67626407373316426256674791352 q^{67} - 236968085984748705579568221704 q^{68} + 104557344970876974303102148968 q^{69} - 128535386121255426052670254680 q^{70} + 82346073793101774211732339984 q^{71} - 318402856717695866548267180524 q^{72} + 493394603638776417802486969216 q^{73} + 403963624337162432162869428448 q^{74} - 90860906848622958011085086226 q^{75} - 4978860022096966736836395728 q^{76} - 283533510170533681316195743872 q^{77} + 1846424319021748888889865208008 q^{78} - 2027941797429451032249224249440 q^{79} + 1950568963732098181450602563404 q^{80} + 3232013063759513061411953049372 q^{81} + 281185962992422454588097491208 q^{82} + 639257677989729325407728993304 q^{83} - 3814583722106892865871881389408 q^{84} + 2937864892869239594066716595632 q^{85} + 2144154326762337104416082819792 q^{86} - 6575908583619059625172760792796 q^{87} - 13387047330534536006261486054136 q^{88} + 9975944419700287698983753923800 q^{89} - 1178333335351272666504645596376 q^{90} - 22910828840952003220639237818160 q^{91} + 29920543982333123076768352679424 q^{92} + 8215357623576313889482958320032 q^{93} + 17399937757784178604603501526168 q^{94} - 17347840986679656809418517646896 q^{95} + 30495307742917507631226680283120 q^{96} + 33857538110974067002078894804912 q^{97} - 9458506231118988779433171599852 q^{98} - 5501751585483871253354308418736 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{32}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.32.a \(\chi_{15}(1, \cdot)\) 15.32.a.a 4 1
15.32.a.b 5
15.32.a.c 5
15.32.a.d 6
15.32.b \(\chi_{15}(4, \cdot)\) 15.32.b.a 32 1
15.32.e \(\chi_{15}(2, \cdot)\) 15.32.e.a 120 2

Decomposition of \(S_{32}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{32}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{32}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{32}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{32}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)