Space of modular forms of level 285 and weight 2

• Label: 285.2
• Level: 285
• Weight: 2
• Dimension: 1871
• Nonzero newspaces: 18
• Newform subspaces: 45
• Sturm bound: 11520
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 45 \)
Sturm bound:			\(11520\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(285))\).

	Total	New	Old
Modular forms	3168	2071	1097
Cusp forms	2593	1871	722
Eisenstein series	575	200	375

Trace form

1871 * q + 5 * q^2 - 15 * q^3 - 27 * q^4 - q^5 - 53 * q^6 - 28 * q^7 + 9 * q^8 - 19 * q^9 - 49 * q^10 + 20 * q^11 - 37 * q^12 - 66 * q^13 - 48 * q^14 - 42 * q^15 - 219 * q^16 - 22 * q^17 - 31 * q^18 - 105 * q^19 - 63 * q^20 - 88 * q^21 - 116 * q^22 - 12 * q^23 - 69 * q^24 - 91 * q^25 - 34 * q^26 - 39 * q^27 - 136 * q^28 - 38 * q^29 - 89 * q^30 - 148 * q^31 - 107 * q^32 - 122 * q^33 - 158 * q^34 - 64 * q^35 - 189 * q^36 - 86 * q^37 - 191 * q^38 - 134 * q^39 - 207 * q^40 - 50 * q^41 - 174 * q^42 - 144 * q^43 - 104 * q^44 - 55 * q^45 - 216 * q^46 - 40 * q^47 + 11 * q^48 - 37 * q^49 - 49 * q^50 + 40 * q^51 + 58 * q^52 + 74 * q^53 + 91 * q^54 - 34 * q^55 + 120 * q^56 + 95 * q^57 + 14 * q^58 + 68 * q^59 + 41 * q^60 - 162 * q^61 - 84 * q^62 + 38 * q^63 - 211 * q^64 - 90 * q^65 - 10 * q^66 - 280 * q^67 - 122 * q^68 - 84 * q^69 - 246 * q^70 - 56 * q^71 + 9 * q^72 - 306 * q^73 - 194 * q^74 - 57 * q^75 - 331 * q^76 - 228 * q^77 - 116 * q^78 - 220 * q^79 + 213 * q^80 + 17 * q^81 - 286 * q^82 + 24 * q^83 + 38 * q^84 + 32 * q^85 + 32 * q^86 + 8 * q^87 + 240 * q^88 - 6 * q^89 + 275 * q^90 - 44 * q^91 + 276 * q^92 + 98 * q^93 + 376 * q^94 + 177 * q^95 + 377 * q^96 + 166 * q^97 + 445 * q^98 + 272 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)

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
285.2.a	\(\chi_{285}(1, \cdot)\)	285.2.a.a	1	1
		285.2.a.b	1
		285.2.a.c	1
		285.2.a.d	2
		285.2.a.e	2
		285.2.a.f	2
		285.2.a.g	2
285.2.b	\(\chi_{285}(284, \cdot)\)	285.2.b.a	4	1
		285.2.b.b	16
		285.2.b.c	16
285.2.c	\(\chi_{285}(229, \cdot)\)	285.2.c.a	6	1
		285.2.c.b	14
285.2.h	\(\chi_{285}(56, \cdot)\)	285.2.h.a	28	1
285.2.i	\(\chi_{285}(106, \cdot)\)	285.2.i.a	2	2
		285.2.i.b	2
		285.2.i.c	2
		285.2.i.d	4
		285.2.i.e	4
		285.2.i.f	10
285.2.k	\(\chi_{285}(77, \cdot)\)	285.2.k.a	4	2
		285.2.k.b	4
		285.2.k.c	28
		285.2.k.d	36
285.2.m	\(\chi_{285}(37, \cdot)\)	285.2.m.a	4	2
		285.2.m.b	36
285.2.p	\(\chi_{285}(221, \cdot)\)	285.2.p.a	4	2
		285.2.p.b	52
285.2.q	\(\chi_{285}(164, \cdot)\)	285.2.q.a	4	2
		285.2.q.b	4
		285.2.q.c	8
		285.2.q.d	56
285.2.r	\(\chi_{285}(49, \cdot)\)	285.2.r.a	40	2
285.2.u	\(\chi_{285}(16, \cdot)\)	285.2.u.a	12	6
		285.2.u.b	18
		285.2.u.c	24
		285.2.u.d	30
285.2.v	\(\chi_{285}(68, \cdot)\)	285.2.v.a	144	4
285.2.x	\(\chi_{285}(88, \cdot)\)	285.2.x.a	80	4
285.2.z	\(\chi_{285}(41, \cdot)\)	285.2.z.a	156	6
285.2.be	\(\chi_{285}(4, \cdot)\)	285.2.be.a	120	6
285.2.bf	\(\chi_{285}(14, \cdot)\)	285.2.bf.a	12	6
		285.2.bf.b	12
		285.2.bf.c	192
285.2.bh	\(\chi_{285}(13, \cdot)\)	285.2.bh.a	240	12
285.2.bi	\(\chi_{285}(17, \cdot)\)	285.2.bi.a	432	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(285))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(285)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)