Space of modular forms of level 36 and weight 6

• Label: 36.6
• Level: 36
• Weight: 6
• Dimension: 78
• Nonzero newspaces: 4
• Newform subspaces: 6
• Sturm bound: 432
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(432\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(36))\).

	Total	New	Old
Modular forms	200	86	114
Cusp forms	160	78	82
Eisenstein series	40	8	32

Trace form

78 * q - 3 * q^2 + 12 * q^3 - 21 * q^4 - 81 * q^5 - 27 * q^6 + 177 * q^7 + 30 * q^9 + 600 * q^10 - 363 * q^11 - 486 * q^12 + 369 * q^13 - 1518 * q^14 + 117 * q^15 - 2169 * q^16 + 1686 * q^17 + 1992 * q^18 - 1428 * q^19 - 1242 * q^20 + 123 * q^21 + 10047 * q^22 + 4503 * q^23 + 2235 * q^24 + 864 * q^25 - 7128 * q^27 - 25284 * q^28 - 17385 * q^29 - 6882 * q^30 - 3309 * q^31 - 7233 * q^32 + 26643 * q^33 + 53997 * q^34 + 41898 * q^35 + 6399 * q^36 - 540 * q^37 - 14877 * q^38 + 5529 * q^39 - 78078 * q^40 - 79197 * q^41 + 18564 * q^42 - 13983 * q^43 - 64131 * q^45 + 57600 * q^46 - 23859 * q^47 - 5931 * q^48 + 102462 * q^49 + 38631 * q^50 + 90612 * q^51 - 55764 * q^52 + 97350 * q^53 + 37587 * q^54 + 43938 * q^55 + 21186 * q^56 - 63852 * q^57 + 78738 * q^58 - 82869 * q^59 + 60930 * q^60 - 136287 * q^61 - 198255 * q^63 - 186486 * q^64 - 89865 * q^65 - 47838 * q^66 + 183 * q^67 + 31413 * q^68 + 212571 * q^69 - 17892 * q^70 + 276240 * q^71 - 130941 * q^72 + 286068 * q^73 - 20406 * q^74 + 44640 * q^75 + 76881 * q^76 - 138285 * q^77 - 96684 * q^78 - 147483 * q^79 - 418962 * q^81 - 263610 * q^82 - 296667 * q^83 + 141630 * q^84 - 393030 * q^85 + 279237 * q^86 + 397323 * q^87 + 226515 * q^88 + 568578 * q^89 + 235278 * q^90 + 445386 * q^91 + 435804 * q^92 + 321879 * q^93 - 223752 * q^94 - 439908 * q^95 - 37476 * q^96 + 277113 * q^97 - 697239 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.6.a	\(\chi_{36}(1, \cdot)\)	36.6.a.a	1	1
		36.6.a.b	1
36.6.b	\(\chi_{36}(35, \cdot)\)	36.6.b.a	2	1
		36.6.b.b	8
36.6.e	\(\chi_{36}(13, \cdot)\)	36.6.e.a	10	2
36.6.h	\(\chi_{36}(11, \cdot)\)	36.6.h.a	56	2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

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