Space of modular forms of level 34 and weight 2

• Label: 34.2
• Level: 34
• Weight: 2
• Dimension: 11
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 144
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 34 = 2 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(34))\).

	Total	New	Old
Modular forms	52	11	41
Cusp forms	21	11	10
Eisenstein series	31	0	31

Trace form

11 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 - 8 * q^7 - q^8 - 13 * q^9 - 2 * q^10 + 4 * q^11 + 4 * q^12 + 2 * q^13 + 8 * q^14 + 24 * q^15 + 3 * q^16 - q^17 + 19 * q^18 - 4 * q^19 - 2 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 4 * q^24 + 5 * q^25 - 10 * q^26 - 16 * q^27 - 8 * q^28 - 10 * q^29 - 24 * q^30 - q^32 - 16 * q^33 - 17 * q^34 - 16 * q^35 - 13 * q^36 - 6 * q^37 - 12 * q^38 + 8 * q^39 - 6 * q^40 + 26 * q^41 + 16 * q^42 + 12 * q^43 + 20 * q^44 + 6 * q^45 + 8 * q^46 + 32 * q^47 - 4 * q^48 + 7 * q^49 + 25 * q^50 - 4 * q^51 + 18 * q^52 + 14 * q^53 + 16 * q^54 + 8 * q^55 - 8 * q^56 + 8 * q^57 + 2 * q^58 + 20 * q^59 + 8 * q^60 - 14 * q^61 + 16 * q^62 - 8 * q^63 - q^64 - 48 * q^65 - 40 * q^66 - 52 * q^67 - 13 * q^68 - 32 * q^69 - 16 * q^70 - 24 * q^71 + 7 * q^72 + 10 * q^73 - 2 * q^74 - 12 * q^75 - 20 * q^76 - 16 * q^77 + 8 * q^78 + 10 * q^80 - 17 * q^81 + 26 * q^82 - 12 * q^83 + 30 * q^85 - 12 * q^86 + 24 * q^87 + 20 * q^88 + 6 * q^89 - 10 * q^90 + 48 * q^91 - 8 * q^92 + 16 * q^94 + 24 * q^95 - 4 * q^96 - 2 * q^97 - 21 * q^98 + 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)

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
34.2.a	\(\chi_{34}(1, \cdot)\)	34.2.a.a	1	1
34.2.b	\(\chi_{34}(33, \cdot)\)	34.2.b.a	2	1
34.2.c	\(\chi_{34}(13, \cdot)\)	34.2.c.a	2	2
		34.2.c.b	2
34.2.d	\(\chi_{34}(9, \cdot)\)	34.2.d.a	4	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(34))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(34)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)