↑

Properties

Label 11.12
Level 11
Weight 12
Dimension 48
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 120
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(11))\).

Total New Old
Modular forms 60 56 4
Cusp forms 50 48 2
Eisenstein series 10 8 2

Trace form

\( 48 q + 43 q^{2} - 509 q^{3} + 2939 q^{4} - 9665 q^{5} - 19429 q^{6} + 129398 q^{7} - 404485 q^{8} + 66891 q^{9} + O(q^{10}) \) \( 48 q + 43 q^{2} - 509 q^{3} + 2939 q^{4} - 9665 q^{5} - 19429 q^{6} + 129398 q^{7} - 404485 q^{8} + 66891 q^{9} + 1231830 q^{10} - 610962 q^{11} - 4439562 q^{12} + 1170536 q^{13} + 11169988 q^{14} - 12479985 q^{15} - 6615097 q^{16} + 28198198 q^{17} - 23483404 q^{18} - 52917060 q^{19} + 40933750 q^{20} + 90120986 q^{21} + 72804193 q^{22} - 18745889 q^{23} - 380476035 q^{24} - 73842565 q^{25} + 480711516 q^{26} + 557150065 q^{27} - 346318706 q^{28} - 876213940 q^{29} - 587961800 q^{30} + 885586751 q^{31} + 823769788 q^{32} + 1122690591 q^{33} - 2002236342 q^{34} - 1565497870 q^{35} + 317992588 q^{36} + 1630761333 q^{37} + 2349238040 q^{38} - 1569618828 q^{39} - 2805776360 q^{40} - 2764303004 q^{41} + 3712489986 q^{42} + 2699628806 q^{43} + 5427209084 q^{44} - 1901804240 q^{45} - 768713294 q^{46} - 6437313312 q^{47} - 7231468724 q^{48} + 42549464 q^{49} + 2494656085 q^{50} + 7668035026 q^{51} + 21274350178 q^{52} - 2404461734 q^{53} - 40129814010 q^{54} - 9035262665 q^{55} + 40829853120 q^{56} + 36770677050 q^{57} - 22943267800 q^{58} - 7545188155 q^{59} - 60838309060 q^{60} - 23766943824 q^{61} - 1602568214 q^{62} + 20659073316 q^{63} + 34965667519 q^{64} + 33264252340 q^{65} + 64959219556 q^{66} + 32916393393 q^{67} - 15040365066 q^{68} - 28034852173 q^{69} - 144044179020 q^{70} - 86171925579 q^{71} - 8801640185 q^{72} - 31663848184 q^{73} + 96857164098 q^{74} + 108749937520 q^{75} + 246393496550 q^{76} + 71849490108 q^{77} + 13155086732 q^{78} - 104301761810 q^{79} - 254433287620 q^{80} - 99365242032 q^{81} - 5770601759 q^{82} - 280271172314 q^{83} - 268480795492 q^{84} + 137342390200 q^{85} + 347503226531 q^{86} + 479255169240 q^{87} + 662244558635 q^{88} + 187676900195 q^{89} - 577145228370 q^{90} - 419955118764 q^{91} - 338693457642 q^{92} - 479456519883 q^{93} - 618001871802 q^{94} - 457242193440 q^{95} + 478704275916 q^{96} + 636878989183 q^{97} + 1498152716884 q^{98} + 1268923814851 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(11))\)

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
11.12.a \(\chi_{11}(1, \cdot)\) 11.12.a.a 3 1
11.12.a.b 5
11.12.c \(\chi_{11}(3, \cdot)\) 11.12.c.a 40 4

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(11))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(11)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)