Space of modular forms of level 96 and weight 9

• Label: 96.9
• Level: 96
• Weight: 9
• Dimension: 854
• Nonzero newspaces: 6
• Newform subspaces: 10
• Sturm bound: 4608
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(4608\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(96))\).

	Total	New	Old
Modular forms	2112	874	1238
Cusp forms	1984	854	1130
Eisenstein series	128	20	108

Trace form

854 * q - 4 * q^3 - 8 * q^4 - 672 * q^5 - 4 * q^6 - 4 * q^7 - 3814 * q^9 - 70008 * q^10 + 39552 * q^11 + 45356 * q^12 - 159912 * q^13 - 291168 * q^14 + 13124 * q^15 + 556752 * q^16 + 309120 * q^17 + 52484 * q^18 - 167560 * q^19 - 1380000 * q^20 - 585348 * q^21 - 12112 * q^22 - 1691136 * q^23 + 310824 * q^24 - 72974 * q^25 - 3364200 * q^26 + 51068 * q^27 + 3615232 * q^28 - 137760 * q^29 + 3966132 * q^30 + 245492 * q^31 - 4840920 * q^32 + 1189140 * q^33 - 8278576 * q^34 + 7247232 * q^35 + 4835584 * q^36 + 6053592 * q^37 + 16322040 * q^38 - 11488196 * q^39 - 1151648 * q^40 - 2419392 * q^41 - 18128864 * q^42 + 194168 * q^43 + 22652136 * q^44 + 18441948 * q^45 - 8 * q^46 - 21819984 * q^48 + 7586394 * q^49 + 5145192 * q^50 + 13835768 * q^51 + 45948136 * q^52 + 38848224 * q^53 + 32802136 * q^54 - 67927680 * q^55 - 56874888 * q^56 - 4551652 * q^57 + 50876272 * q^58 + 44938752 * q^59 - 3478760 * q^60 - 79155240 * q^61 + 43931664 * q^62 + 52142076 * q^63 - 54270272 * q^64 - 39256512 * q^65 - 226680340 * q^66 - 193653512 * q^67 + 1507800 * q^68 + 14777084 * q^69 + 334477888 * q^70 + 159664128 * q^71 + 53585696 * q^72 + 125707444 * q^73 - 56030304 * q^74 + 11356024 * q^75 - 403579912 * q^76 - 40574976 * q^77 - 173869572 * q^78 - 196042236 * q^79 + 360917832 * q^80 + 226330078 * q^81 + 393464392 * q^82 + 209328000 * q^83 + 688968232 * q^84 + 228840112 * q^85 + 18570048 * q^86 - 92085824 * q^87 - 486276128 * q^88 - 261359616 * q^89 - 931912864 * q^90 - 395802248 * q^91 + 152934384 * q^92 - 118704776 * q^93 - 109034752 * q^94 + 367154672 * q^96 + 373369004 * q^97 - 239975856 * q^98 - 543516804 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(96))\)

We only show spaces with odd 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
96.9.b	\(\chi_{96}(79, \cdot)\)	96.9.b.a	16	1
96.9.e	\(\chi_{96}(65, \cdot)\)	96.9.e.a	16	1
		96.9.e.b	16
96.9.g	\(\chi_{96}(31, \cdot)\)	96.9.g.a	8	1
		96.9.g.b	8
96.9.h	\(\chi_{96}(17, \cdot)\)	96.9.h.a	1	1
		96.9.h.b	1
		96.9.h.c	28
96.9.i	\(\chi_{96}(41, \cdot)\)	None	0	2
96.9.l	\(\chi_{96}(7, \cdot)\)	None	0	2
96.9.m	\(\chi_{96}(19, \cdot)\)	96.9.m.a	256	4
96.9.p	\(\chi_{96}(5, \cdot)\)	96.9.p.a	504	4

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(96))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(96)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)