Space of modular forms of level 136 and weight 4

• Label: 136.4
• Level: 136
• Weight: 4
• Dimension: 934
• Nonzero newspaces: 9
• Newform subspaces: 18
• Sturm bound: 4608
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(4608\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(136))\).

	Total	New	Old
Modular forms	1824	994	830
Cusp forms	1632	934	698
Eisenstein series	192	60	132

Trace form

934 * q - 12 * q^2 - 8 * q^3 + 8 * q^4 + 4 * q^5 - 72 * q^6 - 32 * q^7 - 96 * q^8 - 6 * q^9 + 96 * q^10 + 72 * q^11 + 96 * q^12 - 44 * q^13 - 48 * q^14 - 256 * q^15 - 48 * q^16 - 54 * q^17 - 36 * q^18 - 104 * q^19 - 240 * q^20 + 192 * q^21 + 152 * q^22 + 704 * q^23 + 208 * q^24 - 622 * q^25 - 576 * q^26 - 536 * q^27 - 208 * q^28 - 136 * q^29 + 208 * q^30 + 272 * q^31 + 688 * q^32 + 336 * q^33 - 44 * q^34 + 1056 * q^35 - 40 * q^36 + 996 * q^37 + 376 * q^38 + 1376 * q^39 - 464 * q^40 + 184 * q^41 + 432 * q^42 - 1488 * q^43 - 352 * q^44 - 2024 * q^45 - 624 * q^46 - 2416 * q^47 - 928 * q^48 + 618 * q^49 + 36 * q^50 + 184 * q^51 + 1088 * q^52 + 2200 * q^53 + 7728 * q^54 + 4752 * q^55 + 5824 * q^56 + 568 * q^57 + 4240 * q^58 + 1560 * q^59 - 960 * q^60 - 2300 * q^61 - 3264 * q^62 - 6288 * q^63 - 6448 * q^64 - 2916 * q^65 - 13200 * q^66 - 3592 * q^67 - 11976 * q^68 - 6688 * q^69 - 11648 * q^70 - 3824 * q^71 - 9712 * q^72 + 392 * q^73 - 4992 * q^74 - 2568 * q^75 - 240 * q^76 + 3216 * q^77 + 7808 * q^78 + 6272 * q^79 + 12640 * q^80 + 6370 * q^81 + 11144 * q^82 + 5888 * q^83 + 15488 * q^84 - 2504 * q^85 + 4616 * q^86 - 7024 * q^87 - 688 * q^88 - 5164 * q^89 + 1872 * q^90 - 1648 * q^91 - 3664 * q^92 + 576 * q^93 + 1328 * q^94 + 6448 * q^95 + 880 * q^96 - 460 * q^97 - 1132 * q^98 + 6288 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(136))\)

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
136.4.a	\(\chi_{136}(1, \cdot)\)	136.4.a.a	2	1
		136.4.a.b	3
		136.4.a.c	3
		136.4.a.d	4
136.4.b	\(\chi_{136}(33, \cdot)\)	136.4.b.a	6	1
		136.4.b.b	8
136.4.c	\(\chi_{136}(69, \cdot)\)	136.4.c.a	24	1
		136.4.c.b	24
136.4.h	\(\chi_{136}(101, \cdot)\)	136.4.h.a	52	1
136.4.i	\(\chi_{136}(13, \cdot)\)	136.4.i.a	104	2
136.4.k	\(\chi_{136}(81, \cdot)\)	136.4.k.a	14	2
		136.4.k.b	14
136.4.n	\(\chi_{136}(9, \cdot)\)	136.4.n.a	24	4
		136.4.n.b	28
136.4.o	\(\chi_{136}(53, \cdot)\)	136.4.o.a	208	4
136.4.r	\(\chi_{136}(7, \cdot)\)	None	0	8
136.4.s	\(\chi_{136}(3, \cdot)\)	136.4.s.a	8	8
		136.4.s.b	8
		136.4.s.c	400

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(136))\) into lower level spaces

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