Space of modular forms of level 33 and weight 2

• Label: 33.2
• Level: 33
• Weight: 2
• Dimension: 19
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 160
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(160\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(33))\).

	Total	New	Old
Modular forms	60	39	21
Cusp forms	21	19	2
Eisenstein series	39	20	19

Trace form

19 * q - 3 * q^2 - 6 * q^3 - 17 * q^4 - 6 * q^5 - 3 * q^6 - 8 * q^7 + 5 * q^8 + 4 * q^9 + 2 * q^10 - q^11 + 3 * q^12 - 14 * q^13 + 6 * q^14 + 9 * q^15 + 19 * q^16 + 12 * q^17 + 7 * q^18 + 8 * q^20 + 12 * q^21 + 17 * q^22 - 4 * q^23 + 5 * q^24 - q^25 + 8 * q^26 - 21 * q^27 - 16 * q^28 - 10 * q^29 - 18 * q^30 - 22 * q^31 - 43 * q^32 - 26 * q^33 - 34 * q^34 - 8 * q^35 - 7 * q^36 - 8 * q^37 - 10 * q^38 + 6 * q^39 + 10 * q^40 + 18 * q^41 + 6 * q^42 + 16 * q^43 + 33 * q^44 + 29 * q^45 + 48 * q^46 + 22 * q^47 + 39 * q^48 + 43 * q^49 + 17 * q^50 + 32 * q^51 + 22 * q^52 + 16 * q^53 + 7 * q^54 + 4 * q^55 - 30 * q^57 - 10 * q^58 - 30 * q^59 - 22 * q^60 - 22 * q^61 - 36 * q^62 - 28 * q^63 - 37 * q^64 - 24 * q^65 - 43 * q^66 - 38 * q^67 - 26 * q^68 - 19 * q^69 - 4 * q^70 - 12 * q^71 - 25 * q^72 + 6 * q^73 - 24 * q^74 + 9 * q^75 + 40 * q^76 + 2 * q^77 - 2 * q^78 + 40 * q^79 + 24 * q^80 + 4 * q^81 - 26 * q^82 + 46 * q^83 + 4 * q^84 + 12 * q^85 + 8 * q^86 + 30 * q^87 - 15 * q^88 - 10 * q^89 + 42 * q^90 - 12 * q^91 + 2 * q^92 + 43 * q^93 - 4 * q^94 + 30 * q^95 - 3 * q^96 + 12 * q^97 + 49 * q^98 + 14 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)

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
33.2.a	\(\chi_{33}(1, \cdot)\)	33.2.a.a	1	1
33.2.d	\(\chi_{33}(32, \cdot)\)	33.2.d.a	2	1
33.2.e	\(\chi_{33}(4, \cdot)\)	33.2.e.a	4	4
		33.2.e.b	4
33.2.f	\(\chi_{33}(2, \cdot)\)	33.2.f.a	8	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(33)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)