Space of modular forms of level 36 and weight 2

• Label: 36.2
• Level: 36
• Weight: 2
• Dimension: 13
• Nonzero newspaces: 4
• Newform subspaces: 4
• Sturm bound: 144
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(36))\).

	Total	New	Old
Modular forms	56	21	35
Cusp forms	17	13	4
Eisenstein series	39	8	31

Trace form

13 * q - 3 * q^2 - 5 * q^4 - 9 * q^5 - 3 * q^6 - 3 * q^7 - 12 * q^9 - 4 * q^10 - 3 * q^11 + 6 * q^12 - 7 * q^13 + 12 * q^14 + 9 * q^15 + 7 * q^16 + 12 * q^17 + 18 * q^18 + 18 * q^20 - 3 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^24 - 9 * q^25 - 12 * q^28 + 3 * q^29 - 18 * q^30 - 9 * q^31 - 33 * q^32 + 15 * q^33 - 13 * q^34 - 6 * q^35 - 33 * q^36 - 10 * q^37 - 27 * q^38 - 3 * q^39 + 2 * q^40 + 21 * q^41 - 18 * q^42 + 9 * q^43 + 15 * q^45 + 12 * q^46 + 9 * q^47 + 21 * q^48 + 19 * q^49 + 21 * q^50 + 32 * q^52 - 12 * q^53 + 39 * q^54 + 18 * q^55 + 18 * q^56 + 6 * q^57 + 32 * q^58 + 3 * q^59 + 6 * q^60 + 5 * q^61 - 3 * q^63 + 10 * q^64 - 27 * q^65 - 24 * q^66 - 9 * q^67 - 15 * q^68 - 39 * q^69 - 6 * q^70 - 24 * q^71 - 21 * q^72 - 58 * q^73 - 30 * q^74 - 12 * q^75 - 3 * q^76 - 27 * q^77 - 12 * q^78 - 15 * q^79 - 12 * q^81 + 14 * q^82 + 9 * q^83 + 30 * q^84 + 10 * q^85 + 21 * q^86 - 9 * q^87 - 21 * q^88 + 12 * q^89 + 6 * q^90 - 6 * q^91 + 24 * q^92 + 45 * q^93 - 18 * q^94 + 12 * q^95 + 12 * q^96 + 23 * q^97 + 9 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.2.a	\(\chi_{36}(1, \cdot)\)	36.2.a.a	1	1
36.2.b	\(\chi_{36}(35, \cdot)\)	36.2.b.a	2	1
36.2.e	\(\chi_{36}(13, \cdot)\)	36.2.e.a	2	2
36.2.h	\(\chi_{36}(11, \cdot)\)	36.2.h.a	8	2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

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