↑

Properties

Label 81.12
Level 81
Weight 12
Dimension 2084
Nonzero newspaces 4
Newform subspaces 20
Sturm bound 5832
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 81 = 3^{4} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 20 \)
Sturm bound: \(5832\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(81))\).

Total New Old
Modular forms 2727 2140 587
Cusp forms 2619 2084 535
Eisenstein series 108 56 52

Trace form

\( 2084 q - 12 q^{2} - 18 q^{3} - 2068 q^{4} - 2949 q^{5} - 18 q^{6} - 25559 q^{7} + 294897 q^{8} - 18 q^{9} + O(q^{10}) \) \( 2084 q - 12 q^{2} - 18 q^{3} - 2068 q^{4} - 2949 q^{5} - 18 q^{6} - 25559 q^{7} + 294897 q^{8} - 18 q^{9} - 587229 q^{10} + 1594275 q^{11} - 18 q^{12} + 1792681 q^{13} - 5263161 q^{14} - 18 q^{15} - 1757536 q^{16} + 17038269 q^{17} - 28664370 q^{18} + 21011977 q^{19} + 2123355 q^{20} - 131303745 q^{21} + 56831496 q^{22} + 325998597 q^{23} + 279742446 q^{24} - 211716568 q^{25} - 713763339 q^{26} - 190242747 q^{27} + 383617639 q^{28} + 1394600181 q^{29} + 796665006 q^{30} - 496943939 q^{31} - 4567909914 q^{32} - 803698029 q^{33} + 1241358894 q^{34} + 4163221581 q^{35} + 624881646 q^{36} - 1780927721 q^{37} + 1942495050 q^{38} - 18 q^{39} - 1901473851 q^{40} - 6573599853 q^{41} - 1689244983 q^{42} + 7246952857 q^{43} + 12284688849 q^{44} - 9129994992 q^{45} - 18941902953 q^{46} - 4991781981 q^{47} + 16401098025 q^{48} + 10035906330 q^{49} + 45673589706 q^{50} - 557754075 q^{51} - 12709133825 q^{52} - 29650545657 q^{53} - 42468206904 q^{54} - 3127207425 q^{55} + 50831431521 q^{56} + 33073316424 q^{57} + 39106195809 q^{58} - 7535080743 q^{59} - 43881796665 q^{60} - 28561512311 q^{61} - 113255138211 q^{62} - 24162032340 q^{63} + 87082389113 q^{64} + 183035850603 q^{65} + 180869100966 q^{66} - 21704208419 q^{67} - 478855250928 q^{68} - 961769124 q^{69} + 22051202919 q^{70} + 203347560987 q^{71} + 300675760110 q^{72} + 40667932090 q^{73} - 170480436621 q^{74} - 222363281268 q^{75} - 61181113586 q^{76} - 186227727027 q^{77} + 132668259777 q^{78} - 3467151287 q^{79} + 801016069134 q^{80} + 205884074934 q^{81} + 40939611294 q^{82} - 184282130181 q^{83} - 810659036223 q^{84} - 41940738099 q^{85} - 605416499736 q^{86} - 358371281826 q^{87} + 467746171068 q^{88} + 389966618340 q^{89} + 197896518639 q^{90} + 62343683234 q^{91} + 1630291067229 q^{92} + 614660372028 q^{93} + 139386231213 q^{94} - 1761245696253 q^{95} - 1942971726789 q^{96} - 681101418275 q^{97} + 480985624845 q^{98} + 385226801046 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(81))\)

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
81.12.a \(\chi_{81}(1, \cdot)\) 81.12.a.a 6 1
81.12.a.b 6
81.12.a.c 10
81.12.a.d 10
81.12.a.e 10
81.12.c \(\chi_{81}(28, \cdot)\) 81.12.c.a 2 2
81.12.c.b 2
81.12.c.c 2
81.12.c.d 2
81.12.c.e 2
81.12.c.f 4
81.12.c.g 4
81.12.c.h 8
81.12.c.i 8
81.12.c.j 8
81.12.c.k 12
81.12.c.l 12
81.12.c.m 20
81.12.e \(\chi_{81}(10, \cdot)\) 81.12.e.a 192 6
81.12.g \(\chi_{81}(4, \cdot)\) 81.12.g.a 1764 18

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(81))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(81)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)