Space of modular forms of level 456 and weight 2

• Label: 456.2
• Level: 456
• Weight: 2
• Dimension: 2348
• Nonzero newspaces: 18
• Newform subspaces: 47
• Sturm bound: 23040
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 47 \)
Sturm bound:			\(23040\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(456))\).

	Total	New	Old
Modular forms	6192	2484	3708
Cusp forms	5329	2348	2981
Eisenstein series	863	136	727

Trace form

2348 * q + 4 * q^2 - 12 * q^3 - 28 * q^4 + 4 * q^5 - 22 * q^6 - 28 * q^7 - 8 * q^8 - 30 * q^9 - 44 * q^10 - 8 * q^11 - 34 * q^12 + 4 * q^13 - 8 * q^14 - 30 * q^15 - 36 * q^16 + 4 * q^17 - 6 * q^18 - 36 * q^19 + 16 * q^20 - 20 * q^22 + 6 * q^24 - 54 * q^25 + 16 * q^26 - 27 * q^27 - 36 * q^28 + 24 * q^29 - 10 * q^30 - 24 * q^31 - 16 * q^32 + 10 * q^33 - 76 * q^34 + 72 * q^35 - 26 * q^36 + 24 * q^37 - 8 * q^38 + 30 * q^39 - 52 * q^40 + 40 * q^41 - 26 * q^42 + 68 * q^43 + 58 * q^45 - 20 * q^46 + 84 * q^47 - 2 * q^48 - 38 * q^49 + 4 * q^50 + 27 * q^51 - 68 * q^52 + 4 * q^53 - 30 * q^54 - 20 * q^55 + 16 * q^56 - 44 * q^57 - 48 * q^58 - 8 * q^59 - 54 * q^60 - 32 * q^61 - 172 * q^62 - 44 * q^63 - 292 * q^64 - 148 * q^65 - 178 * q^66 - 300 * q^67 - 252 * q^68 - 16 * q^69 - 452 * q^70 - 172 * q^71 - 150 * q^72 - 238 * q^73 - 320 * q^74 - 184 * q^75 - 372 * q^76 - 108 * q^77 - 214 * q^78 - 312 * q^79 - 288 * q^80 - 14 * q^81 - 504 * q^82 - 100 * q^83 - 218 * q^84 + 8 * q^85 - 236 * q^86 - 90 * q^87 - 356 * q^88 - 56 * q^89 - 46 * q^90 - 180 * q^91 - 180 * q^92 - 2 * q^93 - 156 * q^94 + 8 * q^95 - 84 * q^96 - 28 * q^97 - 12 * q^98 - 57 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(456))\)

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
456.2.a	\(\chi_{456}(1, \cdot)\)	456.2.a.a	1	1
		456.2.a.b	1
		456.2.a.c	1
		456.2.a.d	1
		456.2.a.e	2
		456.2.a.f	2
456.2.d	\(\chi_{456}(191, \cdot)\)	None	0	1
456.2.e	\(\chi_{456}(379, \cdot)\)	456.2.e.a	40	1
456.2.f	\(\chi_{456}(113, \cdot)\)	456.2.f.a	10	1
		456.2.f.b	10
456.2.g	\(\chi_{456}(229, \cdot)\)	456.2.g.a	18	1
		456.2.g.b	18
456.2.j	\(\chi_{456}(419, \cdot)\)	456.2.j.a	4	1
		456.2.j.b	8
		456.2.j.c	12
		456.2.j.d	24
		456.2.j.e	24
456.2.k	\(\chi_{456}(151, \cdot)\)	None	0	1
456.2.p	\(\chi_{456}(341, \cdot)\)	456.2.p.a	12	1
		456.2.p.b	64
456.2.q	\(\chi_{456}(49, \cdot)\)	456.2.q.a	2	2
		456.2.q.b	2
		456.2.q.c	2
		456.2.q.d	4
		456.2.q.e	4
		456.2.q.f	6
456.2.t	\(\chi_{456}(31, \cdot)\)	None	0	2
456.2.u	\(\chi_{456}(11, \cdot)\)	456.2.u.a	4	2
		456.2.u.b	4
		456.2.u.c	8
		456.2.u.d	136
456.2.v	\(\chi_{456}(221, \cdot)\)	456.2.v.a	152	2
456.2.y	\(\chi_{456}(259, \cdot)\)	456.2.y.a	80	2
456.2.z	\(\chi_{456}(239, \cdot)\)	None	0	2
456.2.be	\(\chi_{456}(277, \cdot)\)	456.2.be.a	80	2
456.2.bf	\(\chi_{456}(65, \cdot)\)	456.2.bf.a	4	2
		456.2.bf.b	4
		456.2.bf.c	16
		456.2.bf.d	16
456.2.bg	\(\chi_{456}(25, \cdot)\)	456.2.bg.a	12	6
		456.2.bg.b	12
		456.2.bg.c	18
		456.2.bg.d	18
456.2.bj	\(\chi_{456}(29, \cdot)\)	456.2.bj.a	456	6
456.2.bk	\(\chi_{456}(61, \cdot)\)	456.2.bk.a	240	6
456.2.bm	\(\chi_{456}(41, \cdot)\)	456.2.bm.a	60	6
		456.2.bm.b	60
456.2.bp	\(\chi_{456}(67, \cdot)\)	456.2.bp.a	240	6
456.2.br	\(\chi_{456}(23, \cdot)\)	None	0	6
456.2.bs	\(\chi_{456}(79, \cdot)\)	None	0	6
456.2.bu	\(\chi_{456}(35, \cdot)\)	456.2.bu.a	12	6
		456.2.bu.b	12
		456.2.bu.c	432

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(456))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(456)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 2}\)