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

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

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