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Properties

Label 29.10
Level 29
Weight 10
Dimension 301
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 700
Trace bound 1

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(700\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(29))\).

Total New Old
Modular forms 329 327 2
Cusp forms 301 301 0
Eisenstein series 28 26 2

Trace form

\( 301 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 14 q^{7} - 14 q^{8} - 14 q^{9} + O(q^{10}) \) \( 301 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 14 q^{7} - 14 q^{8} - 14 q^{9} - 14 q^{10} - 14 q^{11} - 14 q^{12} - 14 q^{13} - 14 q^{14} - 14 q^{15} - 14 q^{16} - 14 q^{17} - 14 q^{18} - 14 q^{19} + 6445810 q^{20} - 268926 q^{21} - 8526798 q^{22} - 1014538 q^{23} + 24428530 q^{24} + 10563378 q^{25} + 3332546 q^{26} - 14505050 q^{27} - 34420764 q^{28} - 13322526 q^{29} + 5643428 q^{30} + 20767194 q^{31} + 62390258 q^{32} + 33923554 q^{33} - 8225854 q^{34} - 43429302 q^{35} - 181687310 q^{36} - 13704166 q^{37} + 61232178 q^{38} + 131751354 q^{39} - 41373710 q^{40} - 14 q^{41} - 14 q^{42} - 14 q^{43} - 255809764 q^{44} + 275332351 q^{45} + 327426736 q^{46} - 95387082 q^{47} - 779475326 q^{48} - 271527494 q^{49} + 36735188 q^{50} + 302528506 q^{51} + 872172994 q^{52} + 415633603 q^{53} + 301740376 q^{54} - 358091006 q^{55} - 796255712 q^{56} - 591136084 q^{57} - 1581792422 q^{58} - 131921048 q^{59} + 404136810 q^{60} + 552492346 q^{61} + 1485561308 q^{62} + 1792255234 q^{63} + 1398329716 q^{64} + 51891763 q^{65} - 1379805854 q^{66} - 1329334790 q^{67} - 2696397592 q^{68} - 1020713414 q^{69} - 381603614 q^{70} + 3159839634 q^{71} + 6873433084 q^{72} + 156929647 q^{73} - 5453939344 q^{74} - 2855692434 q^{75} - 3224051726 q^{76} - 382470774 q^{77} + 2156075250 q^{78} + 1040606266 q^{79} + 8504781810 q^{80} + 4118565234 q^{81} + 1090438258 q^{82} - 221235742 q^{83} - 4659762296 q^{84} - 3878041118 q^{85} - 7658114268 q^{86} - 3557236074 q^{87} - 5801048092 q^{88} - 593000814 q^{89} + 3141456584 q^{90} + 4346656762 q^{91} + 12182532082 q^{92} + 4404998738 q^{93} + 3714399346 q^{94} + 3941200914 q^{95} - 13641773880 q^{96} + 4490466393 q^{97} + 643679960 q^{98} + 681584078 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(29))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
29.10.a \(\chi_{29}(1, \cdot)\) 29.10.a.a 9 1
29.10.a.b 12
29.10.b \(\chi_{29}(28, \cdot)\) 29.10.b.a 22 1
29.10.d \(\chi_{29}(7, \cdot)\) 29.10.d.a 126 6
29.10.e \(\chi_{29}(4, \cdot)\) 29.10.e.a 132 6