↑

Properties

Label 11.10
Level 11
Weight 10
Dimension 40
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 100
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(100\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(11))\).

Total New Old
Modular forms 50 48 2
Cusp forms 40 40 0
Eisenstein series 10 8 2

Trace form

\( 40 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 7595 q^{6} - 9535 q^{7} + 43515 q^{8} - 4245 q^{9} + O(q^{10}) \) \( 40 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 7595 q^{6} - 9535 q^{7} + 43515 q^{8} - 4245 q^{9} - 100010 q^{10} - 15355 q^{11} + 378870 q^{12} + 118055 q^{13} - 101420 q^{14} - 566115 q^{15} - 1860825 q^{16} + 901585 q^{17} + 2657780 q^{18} + 984820 q^{19} - 2149090 q^{20} - 3889630 q^{21} - 4046495 q^{22} + 1045130 q^{23} + 15687885 q^{24} + 3013015 q^{25} - 7869380 q^{26} - 5422790 q^{27} - 1256810 q^{28} + 5796645 q^{29} + 22764880 q^{30} + 10776685 q^{31} - 74842900 q^{32} + 14949780 q^{33} + 2835210 q^{34} - 11486375 q^{35} - 2395580 q^{36} + 19146575 q^{37} + 56373840 q^{38} + 70496685 q^{39} - 48863040 q^{40} - 58005275 q^{41} - 96329910 q^{42} + 43574250 q^{43} - 24984540 q^{44} - 189052580 q^{45} - 23227910 q^{46} + 81302345 q^{47} + 455101780 q^{48} + 279774325 q^{49} + 113715365 q^{50} - 315865970 q^{51} - 58725990 q^{52} - 71933625 q^{53} - 586344570 q^{54} - 198039445 q^{55} - 291837600 q^{56} + 26365740 q^{57} + 222884480 q^{58} + 600653990 q^{59} + 1391453300 q^{60} + 214672235 q^{61} + 437966770 q^{62} - 289666260 q^{63} - 1805748545 q^{64} - 1365816290 q^{65} - 2172408500 q^{66} - 292525520 q^{67} + 992213030 q^{68} + 1387011560 q^{69} + 1574619620 q^{70} + 1347989025 q^{71} + 3917326135 q^{72} + 1267191385 q^{73} - 1056751710 q^{74} - 3541504760 q^{75} - 5074979610 q^{76} - 3026762895 q^{77} - 2123823940 q^{78} + 1423108015 q^{79} + 5110342700 q^{80} + 5060487090 q^{81} + 4304519345 q^{82} + 1137141720 q^{83} + 1426067180 q^{84} - 2948027485 q^{85} - 5227167885 q^{86} - 6349650570 q^{87} - 7805280725 q^{88} - 1407171360 q^{89} - 1565048130 q^{90} + 3777792495 q^{91} + 12296497870 q^{92} + 11444660985 q^{93} + 7168043110 q^{94} - 111972045 q^{95} - 10577103660 q^{96} - 5458480280 q^{97} - 10931605740 q^{98} - 9006990665 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(11))\)

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
11.10.a \(\chi_{11}(1, \cdot)\) 11.10.a.a 3 1
11.10.a.b 5
11.10.c \(\chi_{11}(3, \cdot)\) 11.10.c.a 32 4