↑

Properties

Label 11.8
Level 11
Weight 8
Dimension 30
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 80
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(80\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(11))\).

Total New Old
Modular forms 40 38 2
Cusp forms 30 30 0
Eisenstein series 10 8 2

Trace form

\( 30 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 1715 q^{6} - 990 q^{7} - 4485 q^{8} + 2865 q^{9} + O(q^{10}) \) \( 30 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 1715 q^{6} - 990 q^{7} - 4485 q^{8} + 2865 q^{9} + 9990 q^{10} + 3290 q^{11} - 16650 q^{12} - 11970 q^{13} - 44780 q^{14} + 61935 q^{15} + 59655 q^{16} - 19760 q^{17} - 188020 q^{18} - 5240 q^{19} + 141830 q^{20} + 185210 q^{21} + 235585 q^{22} - 96805 q^{23} + 80925 q^{24} - 185915 q^{25} - 587300 q^{26} - 455915 q^{27} - 398370 q^{28} + 182070 q^{29} + 1067320 q^{30} + 273695 q^{31} - 249700 q^{32} + 1227225 q^{33} + 1512650 q^{34} + 296890 q^{35} - 2056580 q^{36} - 1585915 q^{37} - 3188520 q^{38} - 2194560 q^{39} - 124760 q^{40} + 1936570 q^{41} + 5003010 q^{42} + 3857870 q^{43} + 4880460 q^{44} + 1265380 q^{45} - 672030 q^{46} - 2529100 q^{47} - 10524260 q^{48} - 6528120 q^{49} - 5951515 q^{50} - 6407330 q^{51} + 3170450 q^{52} + 8872980 q^{53} + 24055110 q^{54} + 10381295 q^{55} + 5368320 q^{56} - 8895330 q^{57} - 16196360 q^{58} - 9600175 q^{59} - 21217300 q^{60} - 9903610 q^{61} + 504010 q^{62} + 8720220 q^{63} + 21909055 q^{64} + 16806160 q^{65} + 23581780 q^{66} + 13139585 q^{67} + 4199510 q^{68} - 11035495 q^{69} - 34934060 q^{70} - 25510635 q^{71} - 28660505 q^{72} + 11895350 q^{73} - 4772670 q^{74} + 22506220 q^{75} + 24958310 q^{76} + 12044250 q^{77} + 16960940 q^{78} - 8608950 q^{79} - 10412260 q^{80} - 34143150 q^{81} - 34459015 q^{82} - 10975110 q^{83} + 6982460 q^{84} + 29032610 q^{85} + 14811675 q^{86} + 27544320 q^{87} + 26444715 q^{88} + 2305905 q^{89} + 695550 q^{90} - 14587180 q^{91} - 6293690 q^{92} + 8175405 q^{93} - 4977370 q^{94} - 29857740 q^{95} + 23929500 q^{96} - 22676955 q^{97} - 26812500 q^{98} - 22507025 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(11))\)

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
11.8.a \(\chi_{11}(1, \cdot)\) 11.8.a.a 2 1
11.8.a.b 4
11.8.c \(\chi_{11}(3, \cdot)\) 11.8.c.a 24 4