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Properties

Label 9.12
Level 9
Weight 12
Dimension 24
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 72
Trace bound 1

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(72\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(9))\).

Total New Old
Modular forms 37 29 8
Cusp forms 29 24 5
Eisenstein series 8 5 3

Trace form

\( 24 q - 87 q^{2} - 12 q^{3} - 5709 q^{4} - 6690 q^{5} + 20583 q^{6} + 80208 q^{7} - 268662 q^{8} + 135504 q^{9} + O(q^{10}) \) \( 24 q - 87 q^{2} - 12 q^{3} - 5709 q^{4} - 6690 q^{5} + 20583 q^{6} + 80208 q^{7} - 268662 q^{8} + 135504 q^{9} + 598272 q^{10} - 1285224 q^{11} + 1027860 q^{12} + 1993482 q^{13} - 2138160 q^{14} - 6358608 q^{15} - 12402033 q^{16} + 31587372 q^{17} + 8682876 q^{18} - 22423992 q^{19} - 5380428 q^{20} + 55012206 q^{21} + 23067111 q^{22} - 103327248 q^{23} - 211100355 q^{24} + 64454136 q^{25} + 408298740 q^{26} - 83699352 q^{27} - 93891588 q^{28} - 164595138 q^{29} - 23582592 q^{30} + 223113816 q^{31} + 295991343 q^{32} + 31338342 q^{33} - 738443115 q^{34} - 246345144 q^{35} - 19984653 q^{36} + 329160288 q^{37} + 2267563587 q^{38} - 1999064976 q^{39} - 2096470824 q^{40} - 875080866 q^{41} + 4171968882 q^{42} + 1087474320 q^{43} - 1508879958 q^{44} + 1749349170 q^{45} + 4673267304 q^{46} - 2601257856 q^{47} - 9335236125 q^{48} - 3660542556 q^{49} - 5696437551 q^{50} + 1736777052 q^{51} + 8295260514 q^{52} + 12717900612 q^{53} + 18127857753 q^{54} + 525774624 q^{55} - 21950029266 q^{56} - 7855424196 q^{57} - 17786993244 q^{58} - 21871135776 q^{59} - 10283356116 q^{60} + 6712066530 q^{61} + 93749877348 q^{62} + 51565206888 q^{63} - 2527339134 q^{64} - 32140271670 q^{65} - 93201828246 q^{66} - 21859852680 q^{67} - 99913140585 q^{68} + 6907292550 q^{69} + 78375656802 q^{70} + 127093320720 q^{71} + 161899013547 q^{72} + 4062188496 q^{73} - 165741990492 q^{74} - 218383044348 q^{75} - 89592389763 q^{76} - 61958337330 q^{77} + 150319870614 q^{78} + 55453127760 q^{79} + 414961963872 q^{80} + 222307104312 q^{81} - 7348822842 q^{82} - 78440398548 q^{83} - 711968015814 q^{84} - 238810904964 q^{85} - 140048966847 q^{86} + 99715491216 q^{87} + 115063627659 q^{88} + 527063391108 q^{89} + 620021743884 q^{90} + 215235126648 q^{91} - 496134212574 q^{92} - 572981484354 q^{93} - 317074813512 q^{94} - 575223807408 q^{95} + 118587589272 q^{96} + 423150430338 q^{97} + 1363519752264 q^{98} + 621154334268 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
9.12.a \(\chi_{9}(1, \cdot)\) 9.12.a.a 1 1
9.12.a.b 1
9.12.a.c 2
9.12.c \(\chi_{9}(4, \cdot)\) 9.12.c.a 20 2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)