Space of modular forms of level 96 and weight 6

• Label: 96.6
• Level: 96
• Weight: 6
• Dimension: 530
• Nonzero newspaces: 6
• Newform subspaces: 14
• Sturm bound: 3072
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(3072\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(96))\).

	Total	New	Old
Modular forms	1344	550	794
Cusp forms	1216	530	686
Eisenstein series	128	20	108

Trace form

530 * q - 2 * q^3 - 8 * q^4 - 76 * q^5 - 4 * q^6 + 188 * q^7 - 50 * q^9 + 392 * q^10 + 1580 * q^12 - 228 * q^13 - 4960 * q^14 - 908 * q^15 - 8368 * q^16 - 1616 * q^17 + 644 * q^18 + 2356 * q^19 + 15200 * q^20 + 2604 * q^21 + 24752 * q^22 - 5016 * q^23 - 21464 * q^24 - 30 * q^25 - 25960 * q^26 + 11194 * q^27 + 4352 * q^28 + 8564 * q^29 + 32564 * q^30 - 64820 * q^31 + 37160 * q^32 - 19384 * q^33 + 12496 * q^34 + 9552 * q^35 + 3264 * q^36 + 18812 * q^37 - 69640 * q^38 + 57068 * q^39 - 62368 * q^40 + 24232 * q^41 - 7264 * q^42 - 63492 * q^43 + 65512 * q^44 + 18064 * q^45 - 8 * q^46 - 65256 * q^47 + 112368 * q^48 - 76714 * q^49 + 137064 * q^50 + 27600 * q^51 - 73496 * q^52 + 174180 * q^53 - 144488 * q^54 - 116680 * q^55 - 150920 * q^56 - 53408 * q^57 - 26000 * q^58 + 57920 * q^59 + 143576 * q^60 - 162516 * q^61 + 175632 * q^62 + 47628 * q^63 + 98368 * q^64 - 127448 * q^65 + 145004 * q^66 + 73388 * q^67 + 310616 * q^68 + 144828 * q^69 + 112576 * q^70 - 15448 * q^71 + 179936 * q^72 - 53844 * q^73 - 426208 * q^74 - 237882 * q^75 - 512008 * q^76 - 325952 * q^77 - 611012 * q^78 + 103036 * q^79 + 584 * q^80 + 54474 * q^81 - 367288 * q^82 + 387560 * q^84 + 376088 * q^85 + 182080 * q^86 - 191360 * q^87 + 622944 * q^88 + 294912 * q^89 + 453536 * q^90 + 32824 * q^91 + 379376 * q^92 - 151608 * q^93 - 297600 * q^94 - 243184 * q^95 - 712976 * q^96 - 255804 * q^97 - 165808 * q^98 + 391180 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(96))\)

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
96.6.a	\(\chi_{96}(1, \cdot)\)	96.6.a.a	1	1
		96.6.a.b	1
		96.6.a.c	1
		96.6.a.d	1
		96.6.a.e	1
		96.6.a.f	1
		96.6.a.g	2
		96.6.a.h	2
96.6.c	\(\chi_{96}(95, \cdot)\)	96.6.c.a	20	1
96.6.d	\(\chi_{96}(49, \cdot)\)	96.6.d.a	10	1
96.6.f	\(\chi_{96}(47, \cdot)\)	96.6.f.a	2	1
		96.6.f.b	16
96.6.j	\(\chi_{96}(25, \cdot)\)	None	0	2
96.6.k	\(\chi_{96}(23, \cdot)\)	None	0	2
96.6.n	\(\chi_{96}(13, \cdot)\)	96.6.n.a	160	4
96.6.o	\(\chi_{96}(11, \cdot)\)	96.6.o.a	312	4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(96))\) into lower level spaces

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