Space of modular forms of level 1296 and weight 2

• Label: 1296.2
• Level: 1296
• Weight: 2
• Dimension: 20484
• Nonzero newspaces: 16
• Sturm bound: 186624
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(186624\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1296))\).

	Total	New	Old
Modular forms	48168	20988	27180
Cusp forms	45145	20484	24661
Eisenstein series	3023	504	2519

Trace form

20484 * 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 - 111 * q^17 - 72 * q^18 - 87 * q^19 - 48 * q^20 - 90 * q^21 - 80 * q^22 - 36 * q^23 - 72 * q^24 - 25 * q^25 - 48 * q^26 - 54 * q^27 - 116 * q^28 - 84 * q^29 - 72 * q^30 - 78 * q^31 - 48 * q^32 - 162 * q^33 - 80 * q^34 - 69 * q^35 - 72 * q^36 - 169 * q^37 - 48 * q^38 - 54 * q^39 - 80 * q^40 - 36 * q^41 - 72 * q^42 - 78 * q^43 - 48 * q^44 - 90 * q^45 - 100 * q^46 - 54 * q^47 - 72 * q^48 - 187 * q^49 - 48 * q^50 - 54 * q^51 - 80 * q^52 - 45 * q^53 - 72 * q^54 - 77 * q^55 + 36 * q^56 - 18 * q^57 - 32 * q^58 - 18 * q^59 - 72 * q^60 - 52 * q^61 + 84 * q^62 - 54 * q^63 - 44 * q^64 - 12 * q^65 - 72 * q^66 - 36 * q^67 + 108 * q^68 - 90 * q^69 + 64 * q^70 + 21 * q^71 - 72 * q^72 + 19 * q^73 + 120 * q^74 - 54 * q^75 + 64 * q^76 + 36 * q^77 - 72 * q^78 - 36 * q^79 + 132 * q^80 - 162 * q^81 - 152 * q^82 - 6 * q^83 - 72 * q^84 - 17 * q^85 + 72 * q^86 - 54 * q^87 - 32 * q^88 + 69 * q^89 - 72 * q^90 - q^91 - 48 * q^92 + 18 * q^93 - 96 * q^94 + 249 * q^95 - 72 * q^96 - 96 * q^97 - 48 * q^98 + 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1296))\)

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
1296.2.a	\(\chi_{1296}(1, \cdot)\)	1296.2.a.a	1	1
		1296.2.a.b	1
		1296.2.a.c	1
		1296.2.a.d	1
		1296.2.a.e	1
		1296.2.a.f	1
		1296.2.a.g	1
		1296.2.a.h	1
		1296.2.a.i	1
		1296.2.a.j	1
		1296.2.a.k	1
		1296.2.a.l	1
		1296.2.a.m	2
		1296.2.a.n	2
		1296.2.a.o	2
		1296.2.a.p	2
		1296.2.a.q	2
1296.2.c	\(\chi_{1296}(1295, \cdot)\)	1296.2.c.a	2	1
		1296.2.c.b	2
		1296.2.c.c	2
		1296.2.c.d	2
		1296.2.c.e	4
		1296.2.c.f	4
		1296.2.c.g	8
1296.2.d	\(\chi_{1296}(649, \cdot)\)	None	0	1
1296.2.f	\(\chi_{1296}(647, \cdot)\)	None	0	1
1296.2.i	\(\chi_{1296}(433, \cdot)\)	1296.2.i.a	2	2
		1296.2.i.b	2
		1296.2.i.c	2
		1296.2.i.d	2
		1296.2.i.e	2
		1296.2.i.f	2
		1296.2.i.g	2
		1296.2.i.h	2
		1296.2.i.i	2
		1296.2.i.j	2
		1296.2.i.k	2
		1296.2.i.l	2
		1296.2.i.m	2
		1296.2.i.n	2
		1296.2.i.o	2
		1296.2.i.p	2
		1296.2.i.q	2
		1296.2.i.r	4
		1296.2.i.s	4
		1296.2.i.t	4
1296.2.k	\(\chi_{1296}(325, \cdot)\)	n/a	184	2
1296.2.l	\(\chi_{1296}(323, \cdot)\)	n/a	184	2
1296.2.p	\(\chi_{1296}(215, \cdot)\)	None	0	2
1296.2.r	\(\chi_{1296}(217, \cdot)\)	None	0	2
1296.2.s	\(\chi_{1296}(431, \cdot)\)	1296.2.s.a	2	2
		1296.2.s.b	2
		1296.2.s.c	2
		1296.2.s.d	2
		1296.2.s.e	2
		1296.2.s.f	2
		1296.2.s.g	4
		1296.2.s.h	4
		1296.2.s.i	4
		1296.2.s.j	8
		1296.2.s.k	8
		1296.2.s.l	8
1296.2.u	\(\chi_{1296}(145, \cdot)\)	n/a	102	6
1296.2.v	\(\chi_{1296}(107, \cdot)\)	n/a	376	4
1296.2.y	\(\chi_{1296}(109, \cdot)\)	n/a	376	4
1296.2.bb	\(\chi_{1296}(73, \cdot)\)	None	0	6
1296.2.bd	\(\chi_{1296}(71, \cdot)\)	None	0	6
1296.2.be	\(\chi_{1296}(143, \cdot)\)	n/a	108	6
1296.2.bg	\(\chi_{1296}(49, \cdot)\)	n/a	954	18
1296.2.bh	\(\chi_{1296}(37, \cdot)\)	n/a	840	12
1296.2.bk	\(\chi_{1296}(35, \cdot)\)	n/a	840	12
1296.2.bn	\(\chi_{1296}(23, \cdot)\)	None	0	18
1296.2.bp	\(\chi_{1296}(25, \cdot)\)	None	0	18
1296.2.bq	\(\chi_{1296}(47, \cdot)\)	n/a	972	18
1296.2.bs	\(\chi_{1296}(11, \cdot)\)	n/a	7704	36
1296.2.bv	\(\chi_{1296}(13, \cdot)\)	n/a	7704	36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1296))\) into lower level spaces

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