Properties

Label 29.9
Level 29
Weight 9
Dimension 266
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 630
Trace bound 1

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(630\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(29))\).

Total New Old
Modular forms 294 294 0
Cusp forms 266 266 0
Eisenstein series 28 28 0

Trace form

\( 266q - 14q^{2} - 14q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 14q^{7} - 14q^{8} - 14q^{9} + O(q^{10}) \) \( 266q - 14q^{2} - 14q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 14q^{7} - 14q^{8} - 14q^{9} - 14q^{10} - 14q^{11} - 14q^{12} - 14q^{13} - 14q^{14} - 14q^{15} - 14q^{16} - 14q^{17} - 14q^{18} - 14q^{19} - 903182q^{20} - 1142890q^{21} + 1214962q^{22} + 906976q^{23} + 1376242q^{24} - 1484378q^{25} - 3198734q^{26} - 3007340q^{27} + 2500918q^{29} + 12569060q^{30} + 3948910q^{31} + 2752498q^{32} - 4279184q^{33} - 8655374q^{34} - 8269058q^{35} - 13590542q^{36} + 2371684q^{37} + 15536626q^{38} + 15800078q^{39} - 14450702q^{40} - 14q^{41} - 14q^{42} - 14q^{43} + 39641224q^{44} - 25719134q^{45} - 75721044q^{46} - 7361774q^{47} + 66270946q^{48} + 55535858q^{49} + 83931400q^{50} + 18760882q^{51} - 36851934q^{52} - 56291774q^{53} - 148527932q^{54} - 123136398q^{55} - 65797452q^{56} + 125522026q^{58} + 38521028q^{59} + 286485626q^{60} + 90084722q^{61} + 102501616q^{62} + 9797746q^{63} - 135941792q^{64} - 136182830q^{65} - 314154302q^{66} - 148930894q^{67} - 145901924q^{68} + 38247538q^{69} + 568279810q^{70} - 15272096q^{71} - 144883592q^{72} - 173627202q^{73} - 255545444q^{74} + 232432956q^{75} + 515307506q^{76} + 300268696q^{77} + 305328114q^{78} + 12839750q^{79} - 375642638q^{80} - 433237854q^{81} - 280333326q^{82} - 286733510q^{83} - 704357696q^{84} - 200319770q^{85} + 179118996q^{87} + 814636004q^{88} + 451397296q^{89} + 982228772q^{90} + 533256766q^{91} + 742339570q^{92} + 78998570q^{93} - 127547406q^{94} - 677800382q^{95} - 431412576q^{96} - 523204570q^{97} - 2321996096q^{98} - 2182815572q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(29))\)

We only show spaces with odd 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
29.9.c \(\chi_{29}(12, \cdot)\) 29.9.c.a 38 2
29.9.f \(\chi_{29}(2, \cdot)\) 29.9.f.a 228 12