↑

Properties

Label 36.22
Level 36
Weight 22
Dimension 341
Nonzero newspaces 4
Sturm bound 1584
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1584\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(36))\).

Total New Old
Modular forms 776 349 427
Cusp forms 736 341 395
Eisenstein series 40 8 32

Trace form

\( 341 q - 3 q^{2} - 6591 q^{3} - 2424085 q^{4} - 38076786 q^{5} + 73477605 q^{6} - 232771614 q^{7} + 12880498491 q^{9} + O(q^{10}) \) \( 341 q - 3 q^{2} - 6591 q^{3} - 2424085 q^{4} - 38076786 q^{5} + 73477605 q^{6} - 232771614 q^{7} + 12880498491 q^{9} - 141983250920 q^{10} - 21700804917 q^{11} - 504668625126 q^{12} - 1332034874504 q^{13} - 3424745318478 q^{14} + 8618233932 q^{15} - 5014312762489 q^{16} + 12763575707700 q^{17} - 21466522965144 q^{18} - 40574171366646 q^{19} + 141949831039398 q^{20} - 184011602068974 q^{21} - 417803086639617 q^{22} + 246375587698986 q^{23} - 892386345342597 q^{24} + 6010435653976794 q^{25} + 640063471033224 q^{27} - 1924509060099012 q^{28} + 2801806575078072 q^{29} + 8525530884295518 q^{30} + 6455124142965120 q^{31} - 27944572626756033 q^{32} - 38555133824774781 q^{33} + 31888390730866189 q^{34} - 25478308452638112 q^{35} + 38419709515797759 q^{36} + 23976497117411794 q^{37} - 84359019735514557 q^{38} + 124326335307105900 q^{39} + 310900571891816002 q^{40} - 579052382035522803 q^{41} - 678424908339383964 q^{42} + 238259563243015737 q^{43} - 66079122470566776 q^{45} + 267104305340688192 q^{46} - 810806930939542230 q^{47} - 230497167810240939 q^{48} + 4182712761619587182 q^{49} - 865280384506117689 q^{50} - 1131170667887059947 q^{51} - 2210637883434619028 q^{52} + 1376537771538239586 q^{53} + 1353726582804026643 q^{54} - 4655262035674351152 q^{55} - 7614355553035252542 q^{56} + 306059621293533267 q^{57} + 5258201339445379762 q^{58} + 1682426330252401557 q^{59} - 14065687510072096830 q^{60} + 20043368953718786722 q^{61} - 813355943934447768 q^{63} - 26993584285092262006 q^{64} + 20978246312986876200 q^{65} - 22190407280094116286 q^{66} - 24651971910265073253 q^{67} + 95395252919689882101 q^{68} + 70990639919519539872 q^{69} + 20998961168874029628 q^{70} - 106165646193221963088 q^{71} + 4203245399524940163 q^{72} - 29887927804635067376 q^{73} - 24453625238657511798 q^{74} - 83917424516084191995 q^{75} - 216411772181135228847 q^{76} - 146734273288444425894 q^{77} + 160788296341194356052 q^{78} - 29410224265008243528 q^{79} + 10568319301670251335 q^{81} - 381024806541957454394 q^{82} - 267129250329228196968 q^{83} + 1148368135166556462846 q^{84} + 1335821118710536864820 q^{85} - 1839358486805015290299 q^{86} - 658613118185527588938 q^{87} + 164654953418084615379 q^{88} + 800397637904136125082 q^{89} + 1111114719811377228558 q^{90} - 502353118025910823512 q^{91} - 4566913194025815329316 q^{92} - 945978224372827589676 q^{93} + 4046517744079082209752 q^{94} - 3255368643766712982768 q^{95} - 1241808753541476270756 q^{96} + 2374160542266916223161 q^{97} + 739798423808190826842 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.22.a \(\chi_{36}(1, \cdot)\) 36.22.a.a 1 1
36.22.a.b 2
36.22.a.c 2
36.22.a.d 4
36.22.b \(\chi_{36}(35, \cdot)\) 36.22.b.a 2 1
36.22.b.b 40
36.22.e \(\chi_{36}(13, \cdot)\) 36.22.e.a 42 2
36.22.h \(\chi_{36}(11, \cdot)\) n/a 248 2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(36)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)