Space of modular forms of level 64 and weight 4

• Label: 64.4
• Level: 64
• Weight: 4
• Dimension: 205
• Nonzero newspaces: 4
• Newform subspaces: 9
• Sturm bound: 1024
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 64 = 2^{6} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1024\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(64))\).

	Total	New	Old
Modular forms	420	227	193
Cusp forms	348	205	143
Eisenstein series	72	22	50

Trace form

205 * q - 8 * q^2 - 6 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 37 * q^9 - 8 * q^10 - 26 * q^11 - 8 * q^12 + 64 * q^13 - 8 * q^14 + 116 * q^15 - 8 * q^16 + 90 * q^17 - 8 * q^18 + 18 * q^19 - 8 * q^20 - 20 * q^21 + 464 * q^22 - 8 * q^23 + 992 * q^24 + 41 * q^25 - 48 * q^26 - 192 * q^27 - 768 * q^28 - 408 * q^29 - 2328 * q^30 - 368 * q^31 - 1248 * q^32 - 988 * q^33 - 1008 * q^34 - 484 * q^35 - 888 * q^36 - 528 * q^37 + 432 * q^38 - 8 * q^39 + 1632 * q^40 + 1014 * q^41 + 3152 * q^42 + 830 * q^43 + 992 * q^44 + 1476 * q^45 - 8 * q^46 + 936 * q^47 - 8 * q^48 + 1049 * q^49 - 2864 * q^50 + 4468 * q^51 - 3320 * q^52 + 400 * q^53 - 1736 * q^54 + 568 * q^55 + 384 * q^56 - 1088 * q^57 + 2368 * q^58 - 4466 * q^59 + 4888 * q^60 - 1088 * q^61 + 2984 * q^62 - 7684 * q^63 + 6040 * q^64 - 2296 * q^65 + 5528 * q^66 - 6030 * q^67 + 2056 * q^68 - 644 * q^69 + 2008 * q^70 - 456 * q^71 - 656 * q^72 + 1014 * q^73 - 2640 * q^74 + 7362 * q^75 - 5960 * q^76 + 3116 * q^77 - 2000 * q^78 + 10072 * q^79 + 4256 * q^80 + 6805 * q^81 + 6952 * q^82 + 2554 * q^83 + 4136 * q^84 + 1648 * q^85 - 528 * q^86 - 8 * q^87 - 3128 * q^88 - 3578 * q^89 - 9368 * q^90 - 3340 * q^91 - 12624 * q^92 - 8384 * q^93 - 8936 * q^94 - 6900 * q^95 - 12928 * q^96 - 9358 * q^97 - 12112 * q^98 - 4750 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.4.a	\(\chi_{64}(1, \cdot)\)	64.4.a.a	1	1
		64.4.a.b	1
		64.4.a.c	1
		64.4.a.d	1
		64.4.a.e	1
64.4.b	\(\chi_{64}(33, \cdot)\)	64.4.b.a	2	1
		64.4.b.b	4
64.4.e	\(\chi_{64}(17, \cdot)\)	64.4.e.a	10	2
64.4.g	\(\chi_{64}(9, \cdot)\)	None	0	4
64.4.i	\(\chi_{64}(5, \cdot)\)	64.4.i.a	184	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

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