Properties

Label 9.11
Level 9
Weight 11
Dimension 22
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 66
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(66\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(9))\).

Total New Old
Modular forms 34 26 8
Cusp forms 26 22 4
Eisenstein series 8 4 4

Trace form

\( 22 q - 3 q^{2} + 51 q^{3} - 197 q^{4} + 4956 q^{5} - 5283 q^{6} - 50584 q^{7} - 3951 q^{9} + O(q^{10}) \) \( 22 q - 3 q^{2} + 51 q^{3} - 197 q^{4} + 4956 q^{5} - 5283 q^{6} - 50584 q^{7} - 3951 q^{9} - 288072 q^{10} + 969 q^{11} + 1031514 q^{12} - 33550 q^{13} - 2134578 q^{14} + 1174770 q^{15} + 4548103 q^{16} - 10430748 q^{18} + 1805930 q^{19} + 14542734 q^{20} + 7893876 q^{21} - 27840177 q^{22} - 9944382 q^{23} + 9173583 q^{24} + 24912097 q^{25} - 10369242 q^{27} - 56089972 q^{28} - 41383956 q^{29} - 67505382 q^{30} + 171784694 q^{31} + 165205143 q^{32} + 47221821 q^{33} - 153994635 q^{34} + 107351775 q^{36} + 176227028 q^{37} - 621662181 q^{38} - 161939274 q^{39} - 132278850 q^{40} + 452543883 q^{41} + 733154220 q^{42} + 19372469 q^{43} - 772291584 q^{45} - 1029327408 q^{46} - 289445970 q^{47} - 411656979 q^{48} + 17748219 q^{49} + 1915252779 q^{50} + 1858869675 q^{51} + 3034651928 q^{52} - 4488556437 q^{54} - 1699435872 q^{55} - 4272894318 q^{56} - 1034132379 q^{57} + 1526356530 q^{58} + 3065773551 q^{59} + 11567968038 q^{60} + 995226278 q^{61} - 4692569886 q^{63} - 7164990230 q^{64} - 11094862926 q^{65} - 5862645990 q^{66} - 478946077 q^{67} + 21469701105 q^{68} + 11337524370 q^{69} + 2304532332 q^{70} - 12325971501 q^{72} - 3972208402 q^{73} - 30101814978 q^{74} - 12481839489 q^{75} + 14574706193 q^{76} + 25001072268 q^{77} + 31785497316 q^{78} + 5982468116 q^{79} - 14104914183 q^{81} - 19567194714 q^{82} - 23396438442 q^{83} - 15587763342 q^{84} + 3979952766 q^{85} + 39111097821 q^{86} + 39360802212 q^{87} + 20940939603 q^{88} - 56325384666 q^{90} - 18520184756 q^{91} - 40885098684 q^{92} + 709626342 q^{93} - 18806972652 q^{94} + 22335455946 q^{95} + 61717992336 q^{96} + 15144621431 q^{97} - 23929366734 q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(9))\)

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
9.11.b \(\chi_{9}(8, \cdot)\) 9.11.b.a 4 1
9.11.d \(\chi_{9}(2, \cdot)\) 9.11.d.a 18 2

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)