Space of modular forms of level 36 and weight 22

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

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 - 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

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

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