Space of modular forms of level 96 and weight 4

• Label: 96.4
• Level: 96
• Weight: 4
• Dimension: 314
• Nonzero newspaces: 6
• Newform subspaces: 12
• Sturm bound: 2048
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(2048\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(96))\).

	Total	New	Old
Modular forms	832	334	498
Cusp forms	704	314	390
Eisenstein series	128	20	108

Trace form

314 * q - 2 * q^3 - 8 * q^4 - 4 * q^5 - 4 * q^6 - 36 * q^7 - 26 * q^9 - 248 * q^10 + 44 * q^12 + 228 * q^13 + 416 * q^14 + 52 * q^15 + 592 * q^16 + 208 * q^17 + 68 * q^18 + 20 * q^19 - 160 * q^20 + 12 * q^21 - 400 * q^22 - 984 * q^23 + 40 * q^24 - 350 * q^25 - 40 * q^26 + 394 * q^27 - 768 * q^28 + 284 * q^29 - 1132 * q^30 + 2124 * q^31 - 1240 * q^32 + 32 * q^33 - 1072 * q^34 + 912 * q^35 + 576 * q^36 - 668 * q^37 + 440 * q^38 - 916 * q^39 + 1632 * q^40 - 1064 * q^41 + 896 * q^42 - 2052 * q^43 + 1000 * q^44 - 584 * q^45 - 8 * q^46 + 408 * q^47 - 2448 * q^48 + 702 * q^49 + 2856 * q^50 + 624 * q^51 + 3304 * q^52 - 1716 * q^53 - 8 * q^54 - 456 * q^55 - 392 * q^56 - 776 * q^57 - 2384 * q^58 - 2752 * q^59 + 344 * q^60 + 2772 * q^61 - 2928 * q^62 - 756 * q^63 - 9920 * q^64 - 2024 * q^65 - 6004 * q^66 - 2452 * q^67 - 5032 * q^68 + 2364 * q^69 - 2816 * q^70 + 1256 * q^71 + 1376 * q^72 + 4796 * q^73 + 6944 * q^74 + 4662 * q^75 + 10232 * q^76 + 64 * q^77 + 6844 * q^78 + 5692 * q^79 + 11336 * q^80 + 4050 * q^81 + 5832 * q^82 + 2408 * q^84 - 1624 * q^85 + 2368 * q^86 - 2336 * q^87 + 608 * q^88 + 2816 * q^90 - 3176 * q^91 - 7696 * q^92 - 5016 * q^93 - 16640 * q^94 - 5104 * q^95 - 4880 * q^96 - 7724 * q^97 - 10288 * q^98 - 9428 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(96))\)

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
96.4.a	\(\chi_{96}(1, \cdot)\)	96.4.a.a	1	1
		96.4.a.b	1
		96.4.a.c	1
		96.4.a.d	1
		96.4.a.e	1
		96.4.a.f	1
96.4.c	\(\chi_{96}(95, \cdot)\)	96.4.c.a	12	1
96.4.d	\(\chi_{96}(49, \cdot)\)	96.4.d.a	6	1
96.4.f	\(\chi_{96}(47, \cdot)\)	96.4.f.a	2	1
		96.4.f.b	8
96.4.j	\(\chi_{96}(25, \cdot)\)	None	0	2
96.4.k	\(\chi_{96}(23, \cdot)\)	None	0	2
96.4.n	\(\chi_{96}(13, \cdot)\)	96.4.n.a	96	4
96.4.o	\(\chi_{96}(11, \cdot)\)	96.4.o.a	184	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(96))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(96)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 1}\)