Space of modular forms of level 510 and weight 2

• Label: 510.2
• Level: 510
• Weight: 2
• Dimension: 1569
• Nonzero newspaces: 18
• Newform subspaces: 60
• Sturm bound: 27648
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 60 \)
Sturm bound:			\(27648\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(510))\).

	Total	New	Old
Modular forms	7424	1569	5855
Cusp forms	6401	1569	4832
Eisenstein series	1023	0	1023

Trace form

1569 * q + q^2 + 5 * q^3 + q^4 + 9 * q^5 + 5 * q^6 + 8 * q^7 + q^8 + q^9 + q^10 + 44 * q^11 + 5 * q^12 + 46 * q^13 + 40 * q^14 + 29 * q^15 + 17 * q^16 + 41 * q^17 + 49 * q^18 + 52 * q^19 + q^20 + 88 * q^21 + 60 * q^22 + 40 * q^23 + 21 * q^24 + 89 * q^25 + 30 * q^26 + 5 * q^27 + 8 * q^28 + 62 * q^29 + 29 * q^30 + 128 * q^31 + q^32 + 60 * q^33 - 15 * q^34 + 40 * q^35 + q^36 + 38 * q^37 - 28 * q^38 - 42 * q^39 - 23 * q^40 + 42 * q^41 - 120 * q^42 + 12 * q^43 - 4 * q^44 - 47 * q^45 - 72 * q^46 - 48 * q^47 - 11 * q^48 - 87 * q^49 - 15 * q^50 - 139 * q^51 - 18 * q^52 - 26 * q^53 - 107 * q^54 + 12 * q^55 - 8 * q^56 - 124 * q^57 - 2 * q^58 + 44 * q^59 - 19 * q^60 + 62 * q^61 - 16 * q^62 + 8 * q^63 + q^64 + 22 * q^65 - 52 * q^66 + 36 * q^67 - 39 * q^68 - 8 * q^69 - 184 * q^70 - 184 * q^71 + q^72 - 342 * q^73 - 186 * q^74 - 187 * q^75 - 44 * q^76 - 288 * q^77 - 138 * q^78 - 288 * q^79 - 87 * q^80 - 47 * q^81 - 294 * q^82 - 236 * q^83 - 72 * q^84 - 591 * q^85 - 196 * q^86 - 346 * q^87 - 132 * q^88 - 358 * q^89 - 47 * q^90 - 528 * q^91 - 88 * q^92 - 320 * q^93 - 272 * q^94 - 412 * q^95 - 11 * q^96 - 382 * q^97 - 183 * q^98 - 148 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(510))\)

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
510.2.a	\(\chi_{510}(1, \cdot)\)	510.2.a.a	1	1
		510.2.a.b	1
		510.2.a.c	1
		510.2.a.d	1
		510.2.a.e	1
		510.2.a.f	1
		510.2.a.g	1
		510.2.a.h	2
510.2.c	\(\chi_{510}(271, \cdot)\)	510.2.c.a	2	1
		510.2.c.b	2
		510.2.c.c	4
		510.2.c.d	4
510.2.d	\(\chi_{510}(409, \cdot)\)	510.2.d.a	2	1
		510.2.d.b	4
		510.2.d.c	4
		510.2.d.d	6
510.2.f	\(\chi_{510}(169, \cdot)\)	510.2.f.a	4	1
		510.2.f.b	4
		510.2.f.c	6
		510.2.f.d	6
510.2.i	\(\chi_{510}(353, \cdot)\)	510.2.i.a	72	2
510.2.l	\(\chi_{510}(137, \cdot)\)	510.2.l.a	4	2
		510.2.l.b	4
		510.2.l.c	4
		510.2.l.d	8
		510.2.l.e	8
		510.2.l.f	8
		510.2.l.g	28
510.2.m	\(\chi_{510}(259, \cdot)\)	510.2.m.a	8	2
		510.2.m.b	8
		510.2.m.c	12
		510.2.m.d	12
510.2.p	\(\chi_{510}(361, \cdot)\)	510.2.p.a	4	2
		510.2.p.b	4
		510.2.p.c	8
		510.2.p.d	8
510.2.q	\(\chi_{510}(203, \cdot)\)	510.2.q.a	72	2
510.2.t	\(\chi_{510}(47, \cdot)\)	510.2.t.a	72	2
510.2.u	\(\chi_{510}(121, \cdot)\)	510.2.u.a	8	4
		510.2.u.b	8
		510.2.u.c	16
		510.2.u.d	16
510.2.w	\(\chi_{510}(257, \cdot)\)	510.2.w.a	4	4
		510.2.w.b	4
		510.2.w.c	68
		510.2.w.d	68
510.2.z	\(\chi_{510}(53, \cdot)\)	510.2.z.a	4	4
		510.2.z.b	4
		510.2.z.c	68
		510.2.z.d	68
510.2.bb	\(\chi_{510}(19, \cdot)\)	510.2.bb.a	32	4
		510.2.bb.b	32
510.2.bd	\(\chi_{510}(7, \cdot)\)	510.2.bd.a	64	8
		510.2.bd.b	80
510.2.bf	\(\chi_{510}(11, \cdot)\)	510.2.bf.a	96	8
		510.2.bf.b	96
510.2.bh	\(\chi_{510}(29, \cdot)\)	510.2.bh.a	144	8
		510.2.bh.b	144
510.2.bi	\(\chi_{510}(37, \cdot)\)	510.2.bi.a	64	8
		510.2.bi.b	80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(510))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(510)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 2}\)