Properties

Label 29.12
Level 29
Weight 12
Dimension 369
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(29))\).

Total New Old
Modular forms 399 395 4
Cusp forms 371 369 2
Eisenstein series 28 26 2

Trace form

\( 369q + 34q^{2} - 518q^{3} + 2930q^{4} - 9674q^{5} + 12082q^{6} + 33474q^{7} - 168974q^{8} + 227272q^{9} + O(q^{10}) \) \( 369q + 34q^{2} - 518q^{3} + 2930q^{4} - 9674q^{5} + 12082q^{6} + 33474q^{7} - 168974q^{8} + 227272q^{9} + 231826q^{10} - 1069238q^{11} + 741874q^{12} + 1155462q^{13} - 803726q^{14} - 2434334q^{15} - 1974286q^{16} + 13811854q^{17} - 5454878q^{18} - 21322854q^{19} + 153328882q^{20} - 167093346q^{21} + 66663218q^{22} + 64988244q^{23} - 105885710q^{24} - 229343136q^{25} - 267381198q^{26} + 442491280q^{27} + 914486244q^{28} + 172096664q^{29} - 842451484q^{30} - 718442186q^{31} - 957153294q^{32} + 165230044q^{33} + 1417756914q^{34} + 1579652774q^{35} - 1507737230q^{36} - 1028331508q^{37} - 1595779150q^{38} + 4316552646q^{39} + 1817389042q^{40} - 616240898q^{41} - 202535438q^{42} + 34251402q^{43} - 7727532900q^{44} + 14467370701q^{45} - 12862957888q^{46} - 13890238810q^{47} + 2408852866q^{48} + 21091080024q^{49} + 28115296884q^{50} + 4683497098q^{51} - 34831031102q^{52} - 24120185567q^{53} - 41157236120q^{54} - 446713582q^{55} + 42937849472q^{56} + 28321399484q^{57} + 85963648042q^{58} + 13088578944q^{59} - 68596113558q^{60} - 60755789122q^{61} - 89277746292q^{62} - 55900121774q^{63} + 34528377044q^{64} + 76344121609q^{65} + 172377226210q^{66} + 86879295746q^{67} - 54105512664q^{68} - 117618687158q^{69} - 263133821790q^{70} + 107859488012q^{71} + 159666961564q^{72} + 56895726741q^{73} - 363775955904q^{74} + 73246958316q^{75} + 345643694578q^{76} + 224459419632q^{77} + 153351379314q^{78} - 100351490282q^{79} - 564054593550q^{80} - 409431355824q^{81} - 149128471086q^{82} + 3645002690q^{83} + 241986762808q^{84} + 375439595902q^{85} + 657775790628q^{86} + 257980476516q^{87} + 253584052196q^{88} - 23097183564q^{89} - 612473083432q^{90} - 548858472274q^{91} - 1037107454990q^{92} - 218615066614q^{93} + 113476385778q^{94} + 421353184434q^{95} + 1243402687800q^{96} + 1161468912527q^{97} + 1168397071576q^{98} - 1040879307220q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(29))\)

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
29.12.a \(\chi_{29}(1, \cdot)\) 29.12.a.a 11 1
29.12.a.b 14
29.12.b \(\chi_{29}(28, \cdot)\) 29.12.b.a 26 1
29.12.d \(\chi_{29}(7, \cdot)\) 29.12.d.a 162 6
29.12.e \(\chi_{29}(4, \cdot)\) 29.12.e.a 156 6

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(29))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(29)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)