Space of modular forms of level 68 and weight 2

• Label: 68.2
• Level: 68
• Weight: 2
• Dimension: 68
• Nonzero newspaces: 5
• Newform subspaces: 6
• Sturm bound: 576
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(576\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(68))\).

	Total	New	Old
Modular forms	184	100	84
Cusp forms	105	68	37
Eisenstein series	79	32	47

Trace form

68 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 24 * q^13 - 8 * q^14 - 24 * q^15 - 24 * q^17 - 16 * q^18 - 8 * q^19 - 8 * q^20 - 40 * q^21 - 8 * q^22 - 8 * q^23 + 8 * q^24 - 4 * q^25 + 24 * q^26 + 24 * q^27 + 40 * q^28 + 4 * q^29 + 56 * q^30 + 32 * q^31 + 32 * q^32 + 32 * q^33 + 56 * q^34 + 32 * q^35 + 56 * q^36 + 16 * q^37 + 32 * q^38 + 16 * q^39 + 56 * q^40 - 20 * q^41 + 40 * q^42 + 8 * q^43 + 24 * q^44 - 28 * q^45 + 8 * q^46 - 40 * q^47 - 32 * q^48 - 48 * q^49 - 32 * q^51 - 16 * q^52 - 36 * q^53 - 24 * q^54 - 16 * q^55 - 48 * q^56 + 32 * q^57 - 64 * q^58 - 16 * q^59 - 112 * q^60 + 16 * q^61 - 64 * q^62 + 24 * q^63 - 56 * q^64 + 76 * q^65 - 96 * q^66 + 16 * q^67 - 96 * q^68 + 48 * q^69 - 80 * q^70 - 112 * q^72 + 52 * q^73 - 56 * q^74 + 16 * q^75 - 64 * q^76 - 112 * q^78 - 16 * q^79 - 24 * q^80 + 24 * q^81 - 48 * q^82 - 20 * q^85 + 64 * q^86 + 56 * q^88 + 8 * q^89 + 72 * q^90 + 16 * q^91 + 104 * q^92 + 16 * q^93 + 88 * q^94 + 48 * q^95 + 144 * q^96 - 16 * q^97 + 128 * q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)

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
68.2.a	\(\chi_{68}(1, \cdot)\)	68.2.a.a	2	1
68.2.b	\(\chi_{68}(33, \cdot)\)	68.2.b.a	2	1
68.2.e	\(\chi_{68}(13, \cdot)\)	68.2.e.a	4	2
68.2.h	\(\chi_{68}(9, \cdot)\)	68.2.h.a	4	4
68.2.i	\(\chi_{68}(3, \cdot)\)	68.2.i.a	8	8
		68.2.i.b	48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(68))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(68)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)