↑

Properties

Label 11.15
Level 11
Weight 15
Dimension 65
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 150
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(150\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(11))\).

Total New Old
Modular forms 75 75 0
Cusp forms 65 65 0
Eisenstein series 10 10 0

Trace form

\( 65 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 715515 q^{6} + 1575010 q^{7} - 7454725 q^{8} + 11568965 q^{9} + O(q^{10}) \) \( 65 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 715515 q^{6} + 1575010 q^{7} - 7454725 q^{8} + 11568965 q^{9} - 25368210 q^{11} + 176783350 q^{12} + 26095660 q^{13} - 707775750 q^{14} + 112200605 q^{15} + 602034335 q^{16} - 117898480 q^{17} - 1464783390 q^{18} - 312644675 q^{19} + 7200625940 q^{20} - 15999623675 q^{22} - 11442083345 q^{23} + 45239874305 q^{24} - 3645103215 q^{25} - 12539107110 q^{26} - 3410681240 q^{27} - 8113875060 q^{28} - 448248840 q^{29} - 46588729580 q^{30} + 36647328505 q^{31} + 5533575420 q^{33} - 184769081990 q^{34} - 121969992120 q^{35} + 901247423670 q^{36} + 348489129425 q^{37} - 686296382260 q^{38} - 1271591675590 q^{39} - 32771062860 q^{40} + 1388348160280 q^{41} + 1274660310830 q^{42} - 2117840974280 q^{44} - 2907364955440 q^{45} + 845675977710 q^{46} + 2512376122380 q^{47} + 4434270020280 q^{48} - 2123137511940 q^{49} - 5396000841345 q^{50} - 3863898507855 q^{51} + 5309769987710 q^{52} + 10868007826770 q^{53} - 11911373931665 q^{55} - 11070652940940 q^{56} + 18601573122465 q^{57} + 6322187444380 q^{58} - 2481343756010 q^{59} - 15916227006740 q^{60} - 11116738289030 q^{61} + 9108734500320 q^{62} + 16954172197290 q^{63} + 15515638942775 q^{64} - 12327177686250 q^{66} - 26084599078875 q^{67} - 40163255299800 q^{68} + 6126350432455 q^{69} + 58485280465460 q^{70} - 10434548535985 q^{71} + 49433858016325 q^{72} + 49225398585780 q^{73} - 115659431324650 q^{74} - 85256958922335 q^{75} + 124185321478480 q^{77} + 171831895311760 q^{78} - 1708076734610 q^{79} - 229663742008700 q^{80} - 163727616512065 q^{81} + 159727234431385 q^{82} + 26463988076165 q^{83} + 56454093682650 q^{84} + 26992332006260 q^{85} - 100886957910205 q^{86} + 69158646095275 q^{88} + 3387540999825 q^{89} - 20038022006720 q^{90} - 386533715873840 q^{91} - 289168965397700 q^{92} + 487167367606545 q^{93} + 543279860205720 q^{94} + 181639455148500 q^{95} - 56860816268540 q^{96} - 182813782633570 q^{97} + 28657217493815 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(11))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
11.15.b \(\chi_{11}(10, \cdot)\) 11.15.b.a 1 1
11.15.b.b 12
11.15.d \(\chi_{11}(2, \cdot)\) 11.15.d.a 52 4