Space of modular forms of level 64 and weight 9

• Label: 64.9
• Level: 64
• Weight: 9
• Dimension: 565
• Nonzero newspaces: 4
• Newform subspaces: 10
• Sturm bound: 2304
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 64 = 2^{6} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(2304\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(64))\).

	Total	New	Old
Modular forms	1060	587	473
Cusp forms	988	565	423
Eisenstein series	72	22	50

Trace form

565 * q - 8 * q^2 - 6 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 6551 * q^9 - 8 * q^10 + 19770 * q^11 - 8 * q^12 - 51400 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 + 154546 * q^17 - 8 * q^18 - 167558 * q^19 - 8 * q^20 - 269900 * q^21 - 1068272 * q^22 + 845564 * q^23 + 322272 * q^24 - 1807211 * q^25 - 3364208 * q^26 - 38664 * q^27 + 3615232 * q^28 + 2132344 * q^29 + 7934312 * q^30 - 16 * q^31 - 4840928 * q^32 - 6597572 * q^33 - 8276528 * q^34 - 426628 * q^35 + 7200392 * q^36 + 431544 * q^37 + 16322032 * q^38 + 7650044 * q^39 - 1151648 * q^40 - 3247114 * q^41 - 35148528 * q^42 - 6314822 * q^43 + 22652128 * q^44 - 12249796 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 + 6369457 * q^49 - 5145200 * q^50 + 84417916 * q^51 - 45948152 * q^52 - 7237448 * q^53 + 79361848 * q^54 - 138980356 * q^55 + 56874880 * q^56 - 17203400 * q^57 - 50876288 * q^58 + 135881658 * q^59 - 163708136 * q^60 + 16294200 * q^61 - 43933720 * q^62 + 96767896 * q^64 - 60985752 * q^65 + 227317848 * q^66 - 246235526 * q^67 + 81864712 * q^68 + 73645108 * q^69 - 92889896 * q^70 + 239496188 * q^71 - 261232784 * q^72 + 47641590 * q^73 - 170028944 * q^74 - 36845386 * q^75 + 159303864 * q^76 - 99681612 * q^77 + 68388208 * q^78 - 144406536 * q^79 + 332920480 * q^80 + 345072245 * q^81 + 69799592 * q^82 + 34471674 * q^83 - 689231320 * q^84 - 146268232 * q^85 - 554580944 * q^86 - 149712644 * q^87 + 45587912 * q^88 + 113890166 * q^89 + 873269992 * q^90 + 76429052 * q^91 + 1093020592 * q^92 + 368941168 * q^93 + 310515736 * q^94 - 16 * q^95 - 468840832 * q^96 - 392821958 * q^97 - 1202501264 * q^98 - 184785790 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.9.c	\(\chi_{64}(63, \cdot)\)	64.9.c.a	1	1
		64.9.c.b	2
		64.9.c.c	2
		64.9.c.d	2
		64.9.c.e	4
		64.9.c.f	4
64.9.d	\(\chi_{64}(31, \cdot)\)	64.9.d.a	4	1
		64.9.d.b	12
64.9.f	\(\chi_{64}(15, \cdot)\)	64.9.f.a	30	2
64.9.h	\(\chi_{64}(7, \cdot)\)	None	0	4
64.9.j	\(\chi_{64}(3, \cdot)\)	64.9.j.a	504	8

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)