Space of modular forms of level 1296 and weight 5

• Label: 1296.5
• Level: 1296
• Weight: 5
• Dimension: 82692
• Nonzero newspaces: 16
• Sturm bound: 466560
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(466560\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(1296))\).

	Total	New	Old
Modular forms	188136	83196	104940
Cusp forms	185112	82692	102420
Eisenstein series	3024	504	2520

Trace form

82692 * q - 48 * q^2 - 54 * q^3 - 80 * q^4 - 60 * q^5 - 72 * q^6 - 60 * q^7 - 48 * q^8 - 18 * q^9 - 116 * q^10 - 36 * q^11 - 72 * q^12 - 100 * q^13 - 48 * q^14 - 54 * q^15 - 80 * q^16 - 105 * q^17 - 72 * q^18 - 87 * q^19 - 48 * q^20 - 90 * q^21 - 80 * q^22 - 36 * q^23 - 72 * q^24 + 605 * q^25 - 48 * q^26 - 54 * q^27 - 116 * q^28 - 3228 * q^29 - 72 * q^30 - 3372 * q^31 - 48 * q^32 - 162 * q^33 - 80 * q^34 - 39 * q^35 - 72 * q^36 + 3215 * q^37 - 48 * q^38 - 54 * q^39 - 80 * q^40 + 6612 * q^41 - 72 * q^42 + 3108 * q^43 - 48 * q^44 - 90 * q^45 - 244 * q^46 - 10836 * q^47 - 72 * q^48 - 2581 * q^49 - 48 * q^50 - 54 * q^51 - 80 * q^52 - 75 * q^53 - 72 * q^54 - 1337 * q^55 - 28860 * q^56 - 18 * q^57 - 33152 * q^58 - 5652 * q^59 - 72 * q^60 + 10460 * q^61 + 51036 * q^62 - 54 * q^63 + 39700 * q^64 + 54036 * q^65 - 72 * q^66 + 11268 * q^67 + 59388 * q^68 - 90 * q^69 + 19936 * q^70 - 51 * q^71 - 72 * q^72 - 13661 * q^73 - 70104 * q^74 - 54 * q^75 - 91520 * q^76 - 68028 * q^77 - 72 * q^78 - 18108 * q^79 - 128028 * q^80 - 162 * q^81 - 34280 * q^82 - 7956 * q^83 - 72 * q^84 + 12997 * q^85 + 95352 * q^86 - 54 * q^87 + 92128 * q^88 - 94617 * q^89 - 72 * q^90 - 80533 * q^91 - 48 * q^92 - 15210 * q^93 + 48 * q^94 + 150879 * q^95 - 72 * q^96 + 78780 * q^97 - 48 * q^98 + 173610 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(1296))\)

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
1296.5.b	\(\chi_{1296}(487, \cdot)\)	None	0	1
1296.5.e	\(\chi_{1296}(161, \cdot)\)	1296.5.e.a	4	1
		1296.5.e.b	4
		1296.5.e.c	6
		1296.5.e.d	8
		1296.5.e.e	8
		1296.5.e.f	8
		1296.5.e.g	8
		1296.5.e.h	12
		1296.5.e.i	12
		1296.5.e.j	24
1296.5.g	\(\chi_{1296}(1135, \cdot)\)	1296.5.g.a	2	1
		1296.5.g.b	2
		1296.5.g.c	4
		1296.5.g.d	4
		1296.5.g.e	4
		1296.5.g.f	8
		1296.5.g.g	8
		1296.5.g.h	8
		1296.5.g.i	8
		1296.5.g.j	16
		1296.5.g.k	16
		1296.5.g.l	16
1296.5.h	\(\chi_{1296}(809, \cdot)\)	None	0	1
1296.5.j	\(\chi_{1296}(485, \cdot)\)	n/a	760	2
1296.5.m	\(\chi_{1296}(163, \cdot)\)	n/a	760	2
1296.5.n	\(\chi_{1296}(377, \cdot)\)	None	0	2
1296.5.o	\(\chi_{1296}(271, \cdot)\)	n/a	192	2
1296.5.q	\(\chi_{1296}(593, \cdot)\)	n/a	190	2
1296.5.t	\(\chi_{1296}(55, \cdot)\)	None	0	2
1296.5.w	\(\chi_{1296}(379, \cdot)\)	n/a	1528	4
1296.5.x	\(\chi_{1296}(53, \cdot)\)	n/a	1528	4
1296.5.z	\(\chi_{1296}(199, \cdot)\)	None	0	6
1296.5.ba	\(\chi_{1296}(127, \cdot)\)	n/a	432	6
1296.5.bc	\(\chi_{1296}(17, \cdot)\)	n/a	426	6
1296.5.bf	\(\chi_{1296}(89, \cdot)\)	None	0	6
1296.5.bi	\(\chi_{1296}(19, \cdot)\)	n/a	3432	12
1296.5.bj	\(\chi_{1296}(125, \cdot)\)	n/a	3432	12
1296.5.bl	\(\chi_{1296}(41, \cdot)\)	None	0	18
1296.5.bm	\(\chi_{1296}(31, \cdot)\)	n/a	3888	18
1296.5.bo	\(\chi_{1296}(65, \cdot)\)	n/a	3870	18
1296.5.br	\(\chi_{1296}(7, \cdot)\)	None	0	18
1296.5.bt	\(\chi_{1296}(43, \cdot)\)	n/a	31032	36
1296.5.bu	\(\chi_{1296}(5, \cdot)\)	n/a	31032	36

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(1296))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(1296)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 25}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 15}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 15}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 2}\)