Space of modular forms of level 128 and weight 12

• Label: 128.12
• Level: 128
• Weight: 12
• Dimension: 3144
• Nonzero newspaces: 5
• Sturm bound: 12288
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 128 = 2^{7} \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 5 \)
Sturm bound:			\(12288\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(128))\).

	Total	New	Old
Modular forms	5712	3192	2520
Cusp forms	5552	3144	2408
Eisenstein series	160	48	112

Trace form

3144 * q - 16 * q^2 - 12 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 12 * q^7 - 16 * q^8 - 20 * q^9 - 16 * q^10 - 12 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 24 * q^17 - 16 * q^18 - 12 * q^19 - 16 * q^20 - 708604 * q^21 - 16 * q^22 - 13479508 * q^23 - 16 * q^24 + 136728764 * q^25 - 16 * q^26 - 133635204 * q^27 - 16 * q^28 - 155346432 * q^29 - 16 * q^30 + 687099616 * q^31 - 16 * q^32 - 440692096 * q^33 - 16 * q^34 - 1064775876 * q^35 - 16 * q^36 + 1045524096 * q^37 - 16 * q^38 + 579959964 * q^39 - 16 * q^40 - 2694964804 * q^41 - 16 * q^42 + 2884696652 * q^43 - 16 * q^44 - 193895340 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 + 7909306948 * q^49 - 36807724864 * q^50 + 223733976 * q^51 + 56046072272 * q^52 + 8402432208 * q^53 - 42243182224 * q^54 - 19122805484 * q^55 - 41745629984 * q^56 + 9050035372 * q^57 + 85948359392 * q^58 + 22992780436 * q^59 + 82490747312 * q^60 - 8603308112 * q^61 - 67461330928 * q^62 - 39697461712 * q^63 - 159579746128 * q^64 - 15079722320 * q^65 + 111222165296 * q^66 + 50706890108 * q^67 + 142040213456 * q^68 + 64772951492 * q^69 - 12530223568 * q^70 - 43677902060 * q^71 - 325692553984 * q^72 - 135658245972 * q^73 - 71681877248 * q^74 + 56217569056 * q^75 + 480084692592 * q^76 + 98756789108 * q^77 - 85561295344 * q^78 - 16 * q^79 - 168509389024 * q^80 - 39490066196 * q^81 - 16 * q^82 - 11370505492 * q^83 - 16 * q^84 + 169346324984 * q^85 - 16 * q^86 + 50128110076 * q^87 - 16 * q^88 - 344460258516 * q^89 - 16 * q^90 - 209413389564 * q^91 - 16 * q^92 + 139378838048 * q^93 - 16 * q^94 + 495219799992 * q^95 - 16 * q^96 + 241282676000 * q^97 - 16 * q^98 - 378702509920 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(128))\)

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
128.12.a	\(\chi_{128}(1, \cdot)\)	128.12.a.a	5	1
		128.12.a.b	5
		128.12.a.c	5
		128.12.a.d	5
		128.12.a.e	6
		128.12.a.f	6
		128.12.a.g	6
		128.12.a.h	6
128.12.b	\(\chi_{128}(65, \cdot)\)	128.12.b.a	2	1
		128.12.b.b	2
		128.12.b.c	8
		128.12.b.d	8
		128.12.b.e	12
		128.12.b.f	12
128.12.e	\(\chi_{128}(33, \cdot)\)	128.12.e.a	42	2
		128.12.e.b	42
128.12.g	\(\chi_{128}(17, \cdot)\)	n/a	172	4
128.12.i	\(\chi_{128}(9, \cdot)\)	None	0	8
128.12.k	\(\chi_{128}(5, \cdot)\)	n/a	2800	16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(128)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 7}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)