Space of modular forms of level 275 and weight 3

• Label: 275.3
• Level: 275
• Weight: 3
• Dimension: 5253
• Nonzero newspaces: 21
• Newform subspaces: 51
• Sturm bound: 18000
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 21 \)
Newform subspaces:			\( 51 \)
Sturm bound:			\(18000\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(275))\).

	Total	New	Old
Modular forms	6280	5623	657
Cusp forms	5720	5253	467
Eisenstein series	560	370	190

Trace form

5253 * q - 45 * q^2 - 45 * q^3 - 45 * q^4 - 60 * q^5 - 49 * q^6 - 30 * q^7 - 25 * q^8 - 35 * q^9 - 60 * q^10 - 92 * q^11 - 150 * q^12 - 60 * q^13 - 50 * q^14 - 60 * q^15 - 157 * q^16 - 180 * q^17 - 310 * q^18 - 215 * q^19 - 340 * q^20 - 184 * q^21 - 165 * q^22 - 125 * q^23 - 55 * q^24 - 74 * q^26 + 120 * q^27 + 380 * q^28 + 120 * q^29 + 420 * q^30 + 121 * q^31 + 520 * q^32 + 250 * q^33 + 530 * q^34 + 160 * q^35 + 58 * q^36 - 95 * q^37 - 760 * q^38 - 790 * q^39 - 1280 * q^40 - 464 * q^41 - 2410 * q^42 - 1400 * q^43 - 2020 * q^44 - 1320 * q^45 - 1674 * q^46 - 1020 * q^47 - 2420 * q^48 - 1120 * q^49 - 200 * q^50 - 579 * q^51 + 50 * q^52 + 250 * q^53 + 1220 * q^54 + 250 * q^55 + 1160 * q^56 + 1765 * q^57 + 2540 * q^58 + 1190 * q^59 + 1980 * q^60 + 1026 * q^61 + 1300 * q^62 + 1870 * q^63 + 2375 * q^64 - 140 * q^65 + 1736 * q^66 + 705 * q^67 + 500 * q^68 + 275 * q^69 - 60 * q^70 - 289 * q^71 + 565 * q^72 + 180 * q^73 - 330 * q^74 + 100 * q^75 - 80 * q^76 - 10 * q^77 + 680 * q^78 + 430 * q^79 + 1620 * q^80 - 237 * q^81 - 95 * q^82 + 165 * q^83 - 590 * q^84 - 1280 * q^85 - 9 * q^86 - 660 * q^87 - 195 * q^88 - 75 * q^89 - 2460 * q^90 - 2184 * q^91 - 3220 * q^92 - 4955 * q^93 - 5720 * q^94 - 1820 * q^95 - 7604 * q^96 - 3550 * q^97 - 5240 * q^98 - 4205 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(275))\)

We only show spaces with odd 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
275.3.c	\(\chi_{275}(76, \cdot)\)	275.3.c.a	1	1
		275.3.c.b	2
		275.3.c.c	2
		275.3.c.d	2
		275.3.c.e	4
		275.3.c.f	8
		275.3.c.g	8
		275.3.c.h	8
275.3.d	\(\chi_{275}(274, \cdot)\)	275.3.d.a	2	1
		275.3.d.b	16
		275.3.d.c	16
275.3.f	\(\chi_{275}(232, \cdot)\)	275.3.f.a	16	2
		275.3.f.b	20
		275.3.f.c	24
275.3.m	\(\chi_{275}(41, \cdot)\)	275.3.m.a	232	4
275.3.o	\(\chi_{275}(79, \cdot)\)	275.3.o.a	232	4
275.3.p	\(\chi_{275}(39, \cdot)\)	275.3.p.a	232	4
275.3.q	\(\chi_{275}(24, \cdot)\)	275.3.q.a	8	4
		275.3.q.b	8
		275.3.q.c	8
		275.3.q.d	8
		275.3.q.e	24
		275.3.q.f	24
		275.3.q.g	56
275.3.r	\(\chi_{275}(19, \cdot)\)	275.3.r.a	232	4
275.3.s	\(\chi_{275}(54, \cdot)\)	275.3.s.a	8	4
		275.3.s.b	224
275.3.u	\(\chi_{275}(61, \cdot)\)	275.3.u.a	232	4
275.3.v	\(\chi_{275}(21, \cdot)\)	275.3.v.a	8	4
		275.3.v.b	224
275.3.w	\(\chi_{275}(116, \cdot)\)	275.3.w.a	232	4
275.3.x	\(\chi_{275}(51, \cdot)\)	275.3.x.a	4	4
		275.3.x.b	4
		275.3.x.c	4
		275.3.x.d	4
		275.3.x.e	4
		275.3.x.f	12
		275.3.x.g	12
		275.3.x.h	28
		275.3.x.i	28
		275.3.x.j	40
275.3.bc	\(\chi_{275}(6, \cdot)\)	275.3.bc.a	232	4
275.3.bd	\(\chi_{275}(139, \cdot)\)	275.3.bd.a	232	4
275.3.be	\(\chi_{275}(42, \cdot)\)	275.3.be.a	464	8
275.3.bh	\(\chi_{275}(37, \cdot)\)	275.3.bh.a	464	8
275.3.bi	\(\chi_{275}(12, \cdot)\)	275.3.bi.a	400	8
275.3.bj	\(\chi_{275}(38, \cdot)\)	275.3.bj.a	464	8
275.3.bk	\(\chi_{275}(82, \cdot)\)	275.3.bk.a	64	8
		275.3.bk.b	80
		275.3.bk.c	128
275.3.bp	\(\chi_{275}(3, \cdot)\)	275.3.bp.a	464	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(275))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(275)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)