Space of modular forms of level 550 and weight 2

• Label: 550.2
• Level: 550
• Weight: 2
• Dimension: 2717
• Nonzero newspaces: 21
• Newform subspaces: 82
• Sturm bound: 36000
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 21 \)
Newform subspaces:			\( 82 \)
Sturm bound:			\(36000\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(550))\).

	Total	New	Old
Modular forms	9560	2717	6843
Cusp forms	8441	2717	5724
Eisenstein series	1119	0	1119

Trace form

2717 * q + 2 * q^2 + 8 * q^3 + 2 * q^4 + 10 * q^5 + 13 * q^6 + 26 * q^7 + 2 * q^8 + 46 * q^9 + 10 * q^10 + 22 * q^11 + 18 * q^12 + 38 * q^13 + 26 * q^14 + 40 * q^15 + 2 * q^16 + 16 * q^17 - 19 * q^18 - 25 * q^19 + 4 * q^21 - 28 * q^22 - 12 * q^23 - 27 * q^24 - 70 * q^25 + 8 * q^26 + 5 * q^27 - 14 * q^28 + 20 * q^29 - 40 * q^30 + 14 * q^31 - 3 * q^32 + 63 * q^33 + 6 * q^34 + 40 * q^35 + 31 * q^36 + 86 * q^37 + 70 * q^38 + 82 * q^39 + 10 * q^40 + 84 * q^41 + 14 * q^42 - 102 * q^43 - 53 * q^44 - 150 * q^45 - 92 * q^46 - 184 * q^47 + 8 * q^48 - 316 * q^49 - 30 * q^50 - 231 * q^51 - 112 * q^52 - 172 * q^53 - 200 * q^54 - 140 * q^55 + 16 * q^56 - 235 * q^57 - 220 * q^58 - 175 * q^59 - 80 * q^60 - 246 * q^61 - 186 * q^62 - 352 * q^63 + 2 * q^64 - 190 * q^65 - 112 * q^66 - 174 * q^67 - 144 * q^68 - 138 * q^69 - 120 * q^70 + 64 * q^71 + 46 * q^72 + 48 * q^73 - 104 * q^74 - 120 * q^75 - 30 * q^76 + 16 * q^77 - 48 * q^78 + 50 * q^79 + 10 * q^80 + 217 * q^81 - 41 * q^82 - 87 * q^83 - 16 * q^84 - 30 * q^85 + 33 * q^86 + 60 * q^87 + 22 * q^88 + 50 * q^89 + 10 * q^90 + 84 * q^91 + 38 * q^92 + 26 * q^93 + 156 * q^94 + 40 * q^95 + 8 * q^96 + 11 * q^97 + 159 * q^98 - 174 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)

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
550.2.a	\(\chi_{550}(1, \cdot)\)	550.2.a.a	1	1
		550.2.a.b	1
		550.2.a.c	1
		550.2.a.d	1
		550.2.a.e	1
		550.2.a.f	1
		550.2.a.g	1
		550.2.a.h	1
		550.2.a.i	1
		550.2.a.j	1
		550.2.a.k	1
		550.2.a.l	1
		550.2.a.m	1
		550.2.a.n	2
550.2.b	\(\chi_{550}(199, \cdot)\)	550.2.b.a	2	1
		550.2.b.b	2
		550.2.b.c	2
		550.2.b.d	2
		550.2.b.e	2
		550.2.b.f	4
550.2.f	\(\chi_{550}(43, \cdot)\)	550.2.f.a	4	2
		550.2.f.b	4
		550.2.f.c	4
		550.2.f.d	8
		550.2.f.e	16
550.2.g	\(\chi_{550}(291, \cdot)\)	550.2.g.a	12	4
		550.2.g.b	48
		550.2.g.c	60
550.2.h	\(\chi_{550}(201, \cdot)\)	550.2.h.a	4	4
		550.2.h.b	4
		550.2.h.c	4
		550.2.h.d	4
		550.2.h.e	4
		550.2.h.f	4
		550.2.h.g	4
		550.2.h.h	4
		550.2.h.i	4
		550.2.h.j	8
		550.2.h.k	8
		550.2.h.l	8
		550.2.h.m	8
		550.2.h.n	8
550.2.i	\(\chi_{550}(31, \cdot)\)	550.2.i.a	4	4
		550.2.i.b	4
		550.2.i.c	4
		550.2.i.d	48
		550.2.i.e	60
550.2.j	\(\chi_{550}(81, \cdot)\)	550.2.j.a	12	4
		550.2.j.b	48
		550.2.j.c	60
550.2.k	\(\chi_{550}(111, \cdot)\)	550.2.k.a	4	4
		550.2.k.b	20
		550.2.k.c	20
		550.2.k.d	24
		550.2.k.e	28
550.2.l	\(\chi_{550}(181, \cdot)\)	550.2.l.a	4	4
		550.2.l.b	4
		550.2.l.c	4
		550.2.l.d	48
		550.2.l.e	60
550.2.n	\(\chi_{550}(59, \cdot)\)	550.2.n.a	120	4
550.2.t	\(\chi_{550}(89, \cdot)\)	550.2.t.a	8	4
		550.2.t.b	40
		550.2.t.c	56
550.2.y	\(\chi_{550}(9, \cdot)\)	550.2.y.a	120	4
550.2.z	\(\chi_{550}(69, \cdot)\)	550.2.z.a	120	4
550.2.ba	\(\chi_{550}(49, \cdot)\)	550.2.ba.a	8	4
		550.2.ba.b	8
		550.2.ba.c	8
		550.2.ba.d	8
		550.2.ba.e	8
		550.2.ba.f	16
		550.2.ba.g	16
550.2.bb	\(\chi_{550}(119, \cdot)\)	550.2.bb.a	120	4
550.2.be	\(\chi_{550}(17, \cdot)\)	550.2.be.a	240	8
550.2.bh	\(\chi_{550}(7, \cdot)\)	550.2.bh.a	32	8
		550.2.bh.b	48
		550.2.bh.c	64
550.2.bi	\(\chi_{550}(87, \cdot)\)	550.2.bi.a	240	8
550.2.bj	\(\chi_{550}(13, \cdot)\)	550.2.bj.a	240	8
550.2.bk	\(\chi_{550}(123, \cdot)\)	550.2.bk.a	240	8
550.2.bp	\(\chi_{550}(63, \cdot)\)	550.2.bp.a	240	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(550))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 2}\)