Space of modular forms of level 36 and weight 8

• Label: 36.8
• Level: 36
• Weight: 8
• Dimension: 111
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 576
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(576\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(36))\).

	Total	New	Old
Modular forms	272	119	153
Cusp forms	232	111	121
Eisenstein series	40	8	32

Trace form

111 * q - 3 * q^2 - 53 * q^4 + 423 * q^5 + 213 * q^6 - 311 * q^7 - 858 * q^9 + 2648 * q^10 + 8097 * q^11 - 18822 * q^12 - 13227 * q^13 + 43482 * q^14 - 7875 * q^15 - 3065 * q^16 + 58764 * q^17 - 72144 * q^18 - 1760 * q^19 + 130806 * q^20 + 3453 * q^21 - 10785 * q^22 + 111999 * q^23 - 330189 * q^24 + 168791 * q^25 + 158760 * q^27 + 490908 * q^28 + 198183 * q^29 - 368442 * q^30 - 94565 * q^31 - 308913 * q^32 - 640731 * q^33 - 811075 * q^34 - 587310 * q^35 + 221439 * q^36 - 376302 * q^37 - 252909 * q^38 + 76641 * q^39 + 3010250 * q^40 + 2282655 * q^41 - 952236 * q^42 + 131917 * q^43 - 721677 * q^45 - 1878624 * q^46 - 1029987 * q^47 - 2579451 * q^48 + 494659 * q^49 - 605697 * q^50 - 967464 * q^51 + 6289652 * q^52 + 1135824 * q^53 + 1785603 * q^54 - 3133494 * q^55 - 3655998 * q^56 - 809760 * q^57 - 10949326 * q^58 + 3053271 * q^59 + 3404058 * q^60 + 4293885 * q^61 + 4217721 * q^63 + 18425866 * q^64 + 3068145 * q^65 - 2771214 * q^66 + 940987 * q^67 + 5210877 * q^68 + 1372605 * q^69 - 28101636 * q^70 - 10350744 * q^71 - 1728093 * q^72 - 12162498 * q^73 - 1590654 * q^74 - 4432044 * q^75 + 36314961 * q^76 + 5159997 * q^77 + 9860532 * q^78 + 12337093 * q^79 + 9836142 * q^81 - 41874106 * q^82 + 2315637 * q^83 + 1298838 * q^84 + 16268962 * q^85 + 16265685 * q^86 - 24976413 * q^87 + 32199891 * q^88 - 42615600 * q^89 - 14605122 * q^90 - 11014174 * q^91 + 17059596 * q^92 - 47647503 * q^93 - 34456128 * q^94 + 2553996 * q^95 - 13783884 * q^96 + 21800193 * q^97 + 69035013 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.8.a	\(\chi_{36}(1, \cdot)\)	36.8.a.a	1	1
		36.8.a.b	1
		36.8.a.c	1
36.8.b	\(\chi_{36}(35, \cdot)\)	36.8.b.a	2	1
		36.8.b.b	12
36.8.e	\(\chi_{36}(13, \cdot)\)	36.8.e.a	14	2
36.8.h	\(\chi_{36}(11, \cdot)\)	36.8.h.a	80	2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(36)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 1}\)