Properties

Label 11.9
Level 11
Weight 9
Dimension 35
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 90
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(90\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 45 45 0
Cusp forms 35 35 0
Eisenstein series 10 10 0

Trace form

\( 35 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} - 4485 q^{6} + 5470 q^{7} - 3845 q^{8} - 21595 q^{9} + O(q^{10}) \) \( 35 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} - 4485 q^{6} + 5470 q^{7} - 3845 q^{8} - 21595 q^{9} + 20890 q^{11} + 89590 q^{12} - 12500 q^{13} - 83030 q^{14} - 255295 q^{15} + 443135 q^{16} + 368200 q^{17} - 316350 q^{18} - 442685 q^{19} - 701700 q^{20} + 1136485 q^{22} + 856055 q^{23} - 426415 q^{24} - 168255 q^{25} + 1690 q^{26} - 495110 q^{27} - 2014380 q^{28} - 795320 q^{29} + 680860 q^{30} + 719005 q^{31} - 1885830 q^{33} - 447590 q^{34} + 8132260 q^{35} + 17517870 q^{36} + 5074985 q^{37} - 7443980 q^{38} - 14657890 q^{39} - 24701940 q^{40} - 13192700 q^{41} - 4352890 q^{42} + 9729040 q^{44} + 22347140 q^{45} + 38601510 q^{46} + 21702760 q^{47} + 22641840 q^{48} - 15500160 q^{49} - 41838705 q^{50} - 41019825 q^{51} - 81977530 q^{52} - 53281310 q^{53} + 64546615 q^{55} + 165476180 q^{56} + 88596375 q^{57} + 52229860 q^{58} + 15865180 q^{59} - 57139340 q^{60} - 29302910 q^{61} - 207755000 q^{62} - 178685550 q^{63} - 173922505 q^{64} + 195025470 q^{66} + 164729145 q^{67} + 335519000 q^{68} + 155055655 q^{69} + 60111620 q^{70} + 40307215 q^{71} - 375829355 q^{72} - 272936400 q^{73} - 400896650 q^{74} - 186096645 q^{75} + 114931540 q^{77} + 499364800 q^{78} + 319699810 q^{79} + 667337940 q^{80} + 254880725 q^{81} - 361559015 q^{82} - 558510965 q^{83} - 721672470 q^{84} - 360970180 q^{85} - 141628605 q^{86} + 414348715 q^{88} + 272650805 q^{89} + 1020614800 q^{90} + 640939240 q^{91} + 7336820 q^{92} - 133516095 q^{93} - 650361480 q^{94} - 641153840 q^{95} - 523100900 q^{96} - 217444180 q^{97} + 100626755 q^{99} + O(q^{100}) \)

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

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
11.9.b \(\chi_{11}(10, \cdot)\) 11.9.b.a 1 1
11.9.b.b 6
11.9.d \(\chi_{11}(2, \cdot)\) 11.9.d.a 28 4