Space of modular forms of level 36 and weight 4

• Label: 36.4
• Level: 36
• Weight: 4
• Dimension: 45
• Nonzero newspaces: 4
• Newform subspaces: 6
• Sturm bound: 288
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(36))\).

	Total	New	Old
Modular forms	128	53	75
Cusp forms	88	45	43
Eisenstein series	40	8	32

Trace form

45 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 + 18 * q^5 + 21 * q^6 + 2 * q^7 + 45 * q^9 - 152 * q^10 + 15 * q^11 - 6 * q^12 + 72 * q^13 - 78 * q^14 - 180 * q^15 + 263 * q^16 - 240 * q^17 - 120 * q^18 - 70 * q^19 - 234 * q^20 - 246 * q^21 - 465 * q^22 + 138 * q^23 + 3 * q^24 + 76 * q^25 + 648 * q^27 + 348 * q^28 + 768 * q^29 + 438 * q^30 + 32 * q^31 + 687 * q^32 - 999 * q^33 - 11 * q^34 - 960 * q^35 + 1023 * q^36 + 306 * q^37 + 891 * q^38 - 36 * q^39 + 250 * q^40 + 651 * q^41 + 732 * q^42 + 581 * q^43 + 1188 * q^45 + 528 * q^46 + 90 * q^47 - 1371 * q^48 - 2092 * q^49 - 1977 * q^50 - 1647 * q^51 - 2588 * q^52 - 2622 * q^53 - 3021 * q^54 - 864 * q^55 - 3006 * q^56 - 243 * q^57 - 86 * q^58 + 1137 * q^59 - 1302 * q^60 + 3078 * q^61 + 1896 * q^63 - 502 * q^64 + 1620 * q^65 + 3114 * q^66 + 119 * q^67 + 4845 * q^68 + 12 * q^69 + 3444 * q^70 + 480 * q^71 + 5475 * q^72 - 1692 * q^73 + 5874 * q^74 + 921 * q^75 - 495 * q^76 + 1818 * q^77 + 2484 * q^78 + 1064 * q^79 + 1833 * q^81 + 358 * q^82 + 576 * q^83 - 5850 * q^84 + 3332 * q^85 - 8331 * q^86 - 1386 * q^87 - 2349 * q^88 - 294 * q^89 - 11202 * q^90 - 344 * q^91 - 8724 * q^92 - 1776 * q^93 - 3192 * q^94 - 3984 * q^95 - 3900 * q^96 - 7041 * q^97 - 1854 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.4.a	\(\chi_{36}(1, \cdot)\)	36.4.a.a	1	1
36.4.b	\(\chi_{36}(35, \cdot)\)	36.4.b.a	2	1
		36.4.b.b	4
36.4.e	\(\chi_{36}(13, \cdot)\)	36.4.e.a	6	2
36.4.h	\(\chi_{36}(11, \cdot)\)	36.4.h.a	8	2
		36.4.h.b	24

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

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