Space of modular forms of level 275 and weight 2

• Label: 275.2
• Level: 275
• Weight: 2
• Dimension: 2536
• Nonzero newspaces: 21
• Newform subspaces: 52
• Sturm bound: 12000
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 21 \)
Newform subspaces:			\( 52 \)
Sturm bound:			\(12000\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(275))\).

	Total	New	Old
Modular forms	3280	2904	376
Cusp forms	2721	2536	185
Eisenstein series	559	368	191

Trace form

2536 * q - 51 * q^2 - 53 * q^3 - 59 * q^4 - 70 * q^5 - 98 * q^6 - 66 * q^7 - 85 * q^8 - 81 * q^9 - 90 * q^10 - 104 * q^11 - 186 * q^12 - 78 * q^13 - 108 * q^14 - 100 * q^15 - 129 * q^16 - 76 * q^17 - 103 * q^18 - 60 * q^19 - 60 * q^20 - 118 * q^21 - 81 * q^22 - 133 * q^23 - 80 * q^24 - 50 * q^25 - 238 * q^26 - 95 * q^27 - 92 * q^28 - 90 * q^29 - 100 * q^30 - 113 * q^31 - 151 * q^32 - 123 * q^33 - 208 * q^34 - 120 * q^35 - 229 * q^36 - 141 * q^37 - 160 * q^38 - 132 * q^39 - 30 * q^40 - 158 * q^41 - 52 * q^42 - 18 * q^43 + 21 * q^44 - 50 * q^45 + 2 * q^46 + 24 * q^47 + 212 * q^48 + 96 * q^49 + 50 * q^50 - 78 * q^51 + 214 * q^52 + 2 * q^53 + 210 * q^54 - 10 * q^55 - 20 * q^56 + 40 * q^57 + 150 * q^58 + 5 * q^59 + 100 * q^60 + 2 * q^61 + 38 * q^62 + 32 * q^63 + 111 * q^64 - 30 * q^65 - 88 * q^66 - 111 * q^67 - 22 * q^68 - 107 * q^69 - 100 * q^70 - 203 * q^71 - 45 * q^72 - 178 * q^73 - 168 * q^74 - 100 * q^75 - 340 * q^76 - 156 * q^77 - 336 * q^78 - 210 * q^79 - 90 * q^80 - 274 * q^81 - 162 * q^82 - 78 * q^83 - 148 * q^84 - 10 * q^85 - 208 * q^86 - 140 * q^87 - 195 * q^88 - 105 * q^89 + 150 * q^90 - 128 * q^91 - 66 * q^92 + 69 * q^93 + 112 * q^94 - 20 * q^95 + 172 * q^96 + 179 * q^97 + 213 * q^98 + 179 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)

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
275.2.a	\(\chi_{275}(1, \cdot)\)	275.2.a.a	1	1
		275.2.a.b	1
		275.2.a.c	2
		275.2.a.d	2
		275.2.a.e	2
		275.2.a.f	2
		275.2.a.g	2
		275.2.a.h	4
275.2.b	\(\chi_{275}(199, \cdot)\)	275.2.b.a	2	1
		275.2.b.b	2
		275.2.b.c	4
		275.2.b.d	4
		275.2.b.e	4
275.2.e	\(\chi_{275}(32, \cdot)\)	275.2.e.a	4	2
		275.2.e.b	4
		275.2.e.c	8
		275.2.e.d	16
275.2.g	\(\chi_{275}(16, \cdot)\)	275.2.g.a	112	4
275.2.h	\(\chi_{275}(26, \cdot)\)	275.2.h.a	8	4
		275.2.h.b	8
		275.2.h.c	16
		275.2.h.d	16
		275.2.h.e	16
275.2.i	\(\chi_{275}(56, \cdot)\)	275.2.i.a	44	4
		275.2.i.b	60
275.2.j	\(\chi_{275}(81, \cdot)\)	275.2.j.a	112	4
275.2.k	\(\chi_{275}(36, \cdot)\)	275.2.k.a	4	4
		275.2.k.b	4
		275.2.k.c	4
		275.2.k.d	100
275.2.l	\(\chi_{275}(31, \cdot)\)	275.2.l.a	4	4
		275.2.l.b	4
		275.2.l.c	4
		275.2.l.d	100
275.2.n	\(\chi_{275}(104, \cdot)\)	275.2.n.a	112	4
275.2.t	\(\chi_{275}(14, \cdot)\)	275.2.t.a	112	4
275.2.y	\(\chi_{275}(34, \cdot)\)	275.2.y.a	40	4
		275.2.y.b	56
275.2.z	\(\chi_{275}(49, \cdot)\)	275.2.z.a	16	4
		275.2.z.b	16
		275.2.z.c	32
275.2.ba	\(\chi_{275}(4, \cdot)\)	275.2.ba.a	112	4
275.2.bb	\(\chi_{275}(9, \cdot)\)	275.2.bb.a	112	4
275.2.bf	\(\chi_{275}(28, \cdot)\)	275.2.bf.a	224	8
275.2.bg	\(\chi_{275}(13, \cdot)\)	275.2.bg.a	224	8
275.2.bl	\(\chi_{275}(17, \cdot)\)	275.2.bl.a	224	8
275.2.bm	\(\chi_{275}(7, \cdot)\)	275.2.bm.a	32	8
		275.2.bm.b	32
		275.2.bm.c	64
275.2.bn	\(\chi_{275}(2, \cdot)\)	275.2.bn.a	224	8
275.2.bo	\(\chi_{275}(87, \cdot)\)	275.2.bo.a	16	8
		275.2.bo.b	208

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(275))\) into lower level spaces

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