Space of modular forms of level 1254 and weight 2

• Label: 1254.2
• Level: 1254
• Weight: 2
• Dimension: 10557
• Nonzero newspaces: 24
• Sturm bound: 172800
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 1254 = 2 \cdot 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(172800\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1254))\).

	Total	New	Old
Modular forms	44640	10557	34083
Cusp forms	41761	10557	31204
Eisenstein series	2879	0	2879

Trace form

10557 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 18 * q^5 + 7 * q^6 + 16 * q^7 - 3 * q^8 + 37 * q^9 + 22 * q^10 + 17 * q^11 + 29 * q^12 + 94 * q^13 + 88 * q^14 + 114 * q^15 - 3 * q^16 + 98 * q^17 + 7 * q^18 + 159 * q^19 + 54 * q^20 + 100 * q^21 + 31 * q^22 + 40 * q^23 - 13 * q^24 + 131 * q^25 + 30 * q^26 - 33 * q^27 + 22 * q^29 - 78 * q^30 + 16 * q^31 - 3 * q^32 - 59 * q^33 - 54 * q^34 + 40 * q^35 - 13 * q^36 - 42 * q^37 - 39 * q^38 + 46 * q^39 - 18 * q^40 - 14 * q^41 - 44 * q^42 + 132 * q^43 + 17 * q^44 - 18 * q^45 + 8 * q^46 + 88 * q^47 - 21 * q^48 + 141 * q^49 - 13 * q^50 - 106 * q^51 + 38 * q^52 - 42 * q^53 - 91 * q^54 + 62 * q^55 - 24 * q^56 - 214 * q^57 + 70 * q^58 - 60 * q^59 - 50 * q^60 + 38 * q^61 + 24 * q^62 - 136 * q^63 - 3 * q^64 + 60 * q^65 + 25 * q^66 + 140 * q^67 + 26 * q^68 - 120 * q^69 + 16 * q^70 + 16 * q^71 + 19 * q^72 + 46 * q^73 - 34 * q^74 + 81 * q^75 - 19 * q^76 + 48 * q^77 + 110 * q^78 + 192 * q^79 + 22 * q^80 + 221 * q^81 + 38 * q^82 + 156 * q^83 + 84 * q^84 + 84 * q^85 + 132 * q^86 + 270 * q^87 + 17 * q^88 + 138 * q^89 + 142 * q^90 - 32 * q^91 + 72 * q^92 + 264 * q^93 + 64 * q^94 + 42 * q^95 - 3 * q^96 - 18 * q^97 + 117 * q^98 - 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1254))\)

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
1254.2.a	\(\chi_{1254}(1, \cdot)\)	1254.2.a.a	1	1
		1254.2.a.b	1
		1254.2.a.c	1
		1254.2.a.d	1
		1254.2.a.e	1
		1254.2.a.f	1
		1254.2.a.g	1
		1254.2.a.h	1
		1254.2.a.i	1
		1254.2.a.j	1
		1254.2.a.k	1
		1254.2.a.l	2
		1254.2.a.m	2
		1254.2.a.n	2
		1254.2.a.o	2
		1254.2.a.p	3
		1254.2.a.q	3
		1254.2.a.r	4
1254.2.b	\(\chi_{1254}(989, \cdot)\)	1254.2.b.a	36	1
		1254.2.b.b	36
1254.2.d	\(\chi_{1254}(683, \cdot)\)	1254.2.d.a	32	1
		1254.2.d.b	32
1254.2.g	\(\chi_{1254}(835, \cdot)\)	1254.2.g.a	20	1
		1254.2.g.b	20
1254.2.i	\(\chi_{1254}(463, \cdot)\)	1254.2.i.a	2	2
		1254.2.i.b	2
		1254.2.i.c	2
		1254.2.i.d	2
		1254.2.i.e	2
		1254.2.i.f	2
		1254.2.i.g	2
		1254.2.i.h	2
		1254.2.i.i	2
		1254.2.i.j	2
		1254.2.i.k	2
		1254.2.i.l	4
		1254.2.i.m	4
		1254.2.i.n	4
		1254.2.i.o	6
		1254.2.i.p	6
		1254.2.i.q	6
		1254.2.i.r	10
		1254.2.i.s	10
1254.2.j	\(\chi_{1254}(115, \cdot)\)	n/a	144	4
1254.2.k	\(\chi_{1254}(373, \cdot)\)	1254.2.k.a	40	2
		1254.2.k.b	40
1254.2.o	\(\chi_{1254}(197, \cdot)\)	n/a	160	2
1254.2.q	\(\chi_{1254}(221, \cdot)\)	n/a	128	2
1254.2.r	\(\chi_{1254}(199, \cdot)\)	n/a	192	6
1254.2.t	\(\chi_{1254}(151, \cdot)\)	n/a	160	4
1254.2.w	\(\chi_{1254}(113, \cdot)\)	n/a	320	4
1254.2.y	\(\chi_{1254}(305, \cdot)\)	n/a	288	4
1254.2.z	\(\chi_{1254}(49, \cdot)\)	n/a	320	8
1254.2.bb	\(\chi_{1254}(89, \cdot)\)	n/a	408	6
1254.2.bd	\(\chi_{1254}(131, \cdot)\)	n/a	480	6
1254.2.bf	\(\chi_{1254}(109, \cdot)\)	n/a	240	6
1254.2.bh	\(\chi_{1254}(179, \cdot)\)	n/a	640	8
1254.2.bj	\(\chi_{1254}(83, \cdot)\)	n/a	640	8
1254.2.bn	\(\chi_{1254}(145, \cdot)\)	n/a	320	8
1254.2.bo	\(\chi_{1254}(25, \cdot)\)	n/a	960	24
1254.2.bp	\(\chi_{1254}(13, \cdot)\)	n/a	960	24
1254.2.br	\(\chi_{1254}(17, \cdot)\)	n/a	1920	24
1254.2.bt	\(\chi_{1254}(53, \cdot)\)	n/a	1920	24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1254))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1254)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(418))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(627))\)\(^{\oplus 2}\)