Space of modular forms of level 36 and weight 3

• Label: 36.3
• Level: 36
• Weight: 3
• Dimension: 28
• Nonzero newspaces: 3
• Newform subspaces: 7
• Sturm bound: 216
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(216\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(36))\).

	Total	New	Old
Modular forms	92	38	54
Cusp forms	52	28	24
Eisenstein series	40	10	30

Trace form

28 * q + q^2 + 3 * q^3 + 3 * q^4 + 11 * q^5 - 9 * q^6 - q^7 - 38 * q^8 - 15 * q^9 - 24 * q^10 - 36 * q^11 - 36 * q^12 - 13 * q^13 - 45 * q^15 + 15 * q^16 - 52 * q^17 + 12 * q^18 + 2 * q^19 + 44 * q^20 + 69 * q^21 + 15 * q^22 + 99 * q^23 + 129 * q^24 + 37 * q^25 + 164 * q^26 + 12 * q^28 - 37 * q^29 + 156 * q^30 - 7 * q^31 + 151 * q^32 - 78 * q^33 + 33 * q^34 - 45 * q^36 - 160 * q^37 - 225 * q^38 + 57 * q^39 - 156 * q^40 - 76 * q^41 - 354 * q^42 - 46 * q^43 - 342 * q^44 + 3 * q^45 - 192 * q^46 - 81 * q^47 - 333 * q^48 + 33 * q^49 - 279 * q^50 - 27 * q^51 - 66 * q^52 + 284 * q^53 + 57 * q^54 + 90 * q^55 + 270 * q^56 + 255 * q^57 + 264 * q^58 + 126 * q^59 + 576 * q^60 + 47 * q^61 + 540 * q^62 + 141 * q^63 + 258 * q^64 + 325 * q^65 + 510 * q^66 + 116 * q^67 + 371 * q^68 + 45 * q^69 + 150 * q^70 - 189 * q^72 + 230 * q^73 - 352 * q^74 - 297 * q^75 - 51 * q^76 - 621 * q^77 - 690 * q^78 + 83 * q^79 - 880 * q^80 - 327 * q^81 - 234 * q^82 - 81 * q^83 - 642 * q^84 - 330 * q^85 - 279 * q^86 - 63 * q^87 + 75 * q^88 - 556 * q^89 + 180 * q^90 - 302 * q^91 + 234 * q^92 - 645 * q^93 + 288 * q^94 - 144 * q^95 + 900 * q^96 - 514 * q^97 + 1024 * q^98 + 171 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)

We only show spaces with odd 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
36.3.c	\(\chi_{36}(17, \cdot)\)	None	0	1
36.3.d	\(\chi_{36}(19, \cdot)\)	36.3.d.a	1	1
		36.3.d.b	1
		36.3.d.c	2
36.3.f	\(\chi_{36}(7, \cdot)\)	36.3.f.a	2	2
		36.3.f.b	2
		36.3.f.c	16
36.3.g	\(\chi_{36}(5, \cdot)\)	36.3.g.a	4	2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

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