Properties

Label 9.10
Level 9
Weight 10
Dimension 19
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 60
Trace bound 1

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(60\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(9))\).

Total New Old
Modular forms 31 24 7
Cusp forms 23 19 4
Eisenstein series 8 5 3

Trace form

\( 19 q + 33 q^{2} - 3 q^{3} - 1709 q^{4} + 3297 q^{5} + 2439 q^{6} - 8275 q^{7} + 7914 q^{8} - 15669 q^{9} + O(q^{10}) \) \( 19 q + 33 q^{2} - 3 q^{3} - 1709 q^{4} + 3297 q^{5} + 2439 q^{6} - 8275 q^{7} + 7914 q^{8} - 15669 q^{9} + 20784 q^{10} + 76542 q^{11} - 241212 q^{12} + 30497 q^{13} + 69240 q^{14} + 723843 q^{15} - 245489 q^{16} - 659898 q^{17} - 1039500 q^{18} - 410146 q^{19} + 2597700 q^{20} - 503475 q^{21} + 856599 q^{22} + 3797535 q^{23} - 2686059 q^{24} - 4085108 q^{25} - 3580332 q^{26} - 6176520 q^{27} + 2438300 q^{28} + 640959 q^{29} + 30713544 q^{30} + 6032921 q^{31} - 5115105 q^{32} - 19931472 q^{33} - 7940187 q^{34} - 22987434 q^{35} - 48894093 q^{36} + 2881694 q^{37} + 58248867 q^{38} + 74528535 q^{39} + 15384192 q^{40} + 66324306 q^{41} + 25242354 q^{42} - 28833664 q^{43} - 329694294 q^{44} - 139865967 q^{45} + 5548872 q^{46} + 105014409 q^{47} + 312045027 q^{48} + 155825946 q^{49} + 300455169 q^{50} + 3098385 q^{51} - 205040278 q^{52} - 620105112 q^{53} - 591710103 q^{54} - 41851194 q^{55} + 541484430 q^{56} + 581271465 q^{57} + 379004532 q^{58} + 414160698 q^{59} - 430082172 q^{60} - 195836953 q^{61} - 653251740 q^{62} - 693544725 q^{63} - 615962942 q^{64} + 331127871 q^{65} + 1912534074 q^{66} + 500930204 q^{67} + 778094271 q^{68} - 724756329 q^{69} - 692578974 q^{70} - 1159088256 q^{71} - 1729340037 q^{72} + 624331352 q^{73} + 585481836 q^{74} + 1477690413 q^{75} + 1057924541 q^{76} + 531715125 q^{77} + 243023958 q^{78} - 796354753 q^{79} - 3191808192 q^{80} - 1055378241 q^{81} - 175853706 q^{82} + 2196856275 q^{83} + 1383634866 q^{84} + 290086758 q^{85} + 1686684801 q^{86} + 617958567 q^{87} + 630596235 q^{88} - 3407914980 q^{89} - 981417492 q^{90} - 1264584770 q^{91} + 351721074 q^{92} - 552731577 q^{93} - 2559955728 q^{94} + 608262324 q^{95} + 1854064512 q^{96} + 1361090372 q^{97} + 3323702880 q^{98} + 1672014609 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)

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
9.10.a \(\chi_{9}(1, \cdot)\) 9.10.a.a 1 1
9.10.a.b 1
9.10.a.c 1
9.10.c \(\chi_{9}(4, \cdot)\) 9.10.c.a 16 2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)