Space of modular forms of level 136 and weight 2

• Label: 136.2
• Level: 136
• Weight: 2
• Dimension: 292
• Nonzero newspaces: 9
• Newform subspaces: 21
• Sturm bound: 2304
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(2304\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(136))\).

	Total	New	Old
Modular forms	672	352	320
Cusp forms	481	292	189
Eisenstein series	191	60	131

Trace form

292 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 32 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 32 * q^17 - 32 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 52 * q^25 - 16 * q^26 - 40 * q^27 - 16 * q^28 - 20 * q^29 - 16 * q^30 - 48 * q^31 - 16 * q^32 - 64 * q^33 - 16 * q^34 - 64 * q^35 - 16 * q^36 - 32 * q^37 - 16 * q^38 - 48 * q^39 - 16 * q^40 - 52 * q^41 - 16 * q^42 - 40 * q^43 - 16 * q^44 - 20 * q^45 - 16 * q^46 - 16 * q^47 + 32 * q^48 - 32 * q^49 - 16 * q^50 - 16 * q^51 - 32 * q^52 + 12 * q^53 + 64 * q^54 + 32 * q^55 + 64 * q^56 - 8 * q^57 + 96 * q^58 + 32 * q^59 + 192 * q^60 + 48 * q^61 + 96 * q^62 + 128 * q^63 + 80 * q^64 - 20 * q^65 + 192 * q^66 + 48 * q^67 + 160 * q^68 + 96 * q^69 + 160 * q^70 + 32 * q^71 + 192 * q^72 - 20 * q^73 + 80 * q^74 + 128 * q^75 + 96 * q^76 + 48 * q^77 + 192 * q^78 + 32 * q^79 + 96 * q^80 - 8 * q^81 + 64 * q^82 + 24 * q^83 + 64 * q^84 - 20 * q^85 - 32 * q^86 - 64 * q^87 - 16 * q^88 - 80 * q^89 + 64 * q^90 - 80 * q^91 - 16 * q^92 - 64 * q^93 - 16 * q^94 - 96 * q^95 - 16 * q^96 - 64 * q^97 - 16 * q^98 - 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)

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
136.2.a	\(\chi_{136}(1, \cdot)\)	136.2.a.a	1	1
		136.2.a.b	1
		136.2.a.c	2
136.2.b	\(\chi_{136}(33, \cdot)\)	136.2.b.a	2	1
		136.2.b.b	2
136.2.c	\(\chi_{136}(69, \cdot)\)	136.2.c.a	8	1
		136.2.c.b	8
136.2.h	\(\chi_{136}(101, \cdot)\)	136.2.h.a	16	1
136.2.i	\(\chi_{136}(13, \cdot)\)	136.2.i.a	8	2
		136.2.i.b	24
136.2.k	\(\chi_{136}(81, \cdot)\)	136.2.k.a	2	2
		136.2.k.b	2
		136.2.k.c	2
		136.2.k.d	2
136.2.n	\(\chi_{136}(9, \cdot)\)	136.2.n.a	4	4
		136.2.n.b	4
		136.2.n.c	12
136.2.o	\(\chi_{136}(53, \cdot)\)	136.2.o.a	64	4
136.2.r	\(\chi_{136}(7, \cdot)\)	None	0	8
136.2.s	\(\chi_{136}(3, \cdot)\)	136.2.s.a	8	8
		136.2.s.b	8
		136.2.s.c	112

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(136))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(136)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)