↑

Properties

Label 29.6
Level 29
Weight 6
Dimension 161
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 420
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(420\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(29))\).

Total New Old
Modular forms 189 187 2
Cusp forms 161 161 0
Eisenstein series 28 26 2

Trace form

\( 161 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 14 q^{7} - 14 q^{8} - 14 q^{9} + O(q^{10}) \) \( 161 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 14 q^{7} - 14 q^{8} - 14 q^{9} - 14 q^{10} - 14 q^{11} - 14 q^{12} - 14 q^{13} - 14 q^{14} - 14 q^{15} - 14 q^{16} - 14 q^{17} - 14 q^{18} - 14 q^{19} - 13790 q^{20} + 6846 q^{21} + 16674 q^{22} + 7980 q^{23} + 26866 q^{24} - 882 q^{25} - 13314 q^{26} - 27272 q^{27} - 43932 q^{28} - 21154 q^{29} - 46732 q^{30} - 5754 q^{31} + 14322 q^{32} + 31948 q^{33} + 42686 q^{34} + 42518 q^{35} + 127666 q^{36} + 14840 q^{37} - 1246 q^{38} - 56154 q^{39} - 106190 q^{40} - 14 q^{41} - 14 q^{42} - 14 q^{43} - 114660 q^{44} - 116249 q^{45} - 4144 q^{46} + 52934 q^{47} + 313474 q^{48} + 163002 q^{49} + 239988 q^{50} + 90202 q^{51} + 63938 q^{52} - 32837 q^{53} - 193928 q^{54} - 266686 q^{55} - 291424 q^{56} - 181972 q^{57} - 536102 q^{58} - 78120 q^{59} - 346710 q^{60} - 58758 q^{61} + 17724 q^{62} + 172354 q^{63} + 366772 q^{64} + 262003 q^{65} + 573538 q^{66} + 314202 q^{67} + 531048 q^{68} + 241402 q^{69} - 239694 q^{70} - 372988 q^{71} - 610820 q^{72} - 430661 q^{73} + 135744 q^{74} + 487116 q^{75} + 786674 q^{76} + 435456 q^{77} + 537138 q^{78} + 83174 q^{79} + 185010 q^{80} - 124446 q^{81} - 170478 q^{82} - 264838 q^{83} - 1022168 q^{84} - 585578 q^{85} - 1035468 q^{86} - 511644 q^{87} - 1126300 q^{88} - 391944 q^{89} - 568456 q^{90} - 174818 q^{91} + 29554 q^{92} + 146762 q^{93} + 286482 q^{94} + 839874 q^{95} + 384552 q^{96} - 672455 q^{97} + 772408 q^{98} + 905996 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(29))\)

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
29.6.a \(\chi_{29}(1, \cdot)\) 29.6.a.a 4 1
29.6.a.b 7
29.6.b \(\chi_{29}(28, \cdot)\) 29.6.b.a 12 1
29.6.d \(\chi_{29}(7, \cdot)\) 29.6.d.a 66 6
29.6.e \(\chi_{29}(4, \cdot)\) 29.6.e.a 72 6