Space of modular forms of level 700 and weight 2

• Label: 700.2
• Level: 700
• Weight: 2
• Dimension: 7214
• Nonzero newspaces: 24
• Newform subspaces: 88
• Sturm bound: 57600
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 88 \)
Sturm bound:			\(57600\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(700))\).

	Total	New	Old
Modular forms	15240	7626	7614
Cusp forms	13561	7214	6347
Eisenstein series	1679	412	1267

Trace form

7214 * q - 27 * q^2 - 9 * q^3 - 19 * q^4 - 66 * q^5 - 24 * q^6 - 39 * q^8 - 32 * q^9 - 16 * q^10 + 3 * q^11 - 4 * q^12 - 28 * q^13 - 17 * q^14 + 4 * q^15 - 47 * q^16 - 21 * q^17 - 37 * q^18 + 25 * q^19 - 36 * q^20 - 67 * q^21 - 70 * q^22 + 61 * q^23 - 48 * q^24 + 30 * q^25 - 60 * q^26 + 138 * q^27 - 53 * q^28 + 8 * q^29 - 28 * q^30 + 79 * q^31 + 13 * q^32 + 137 * q^33 - 40 * q^34 + 44 * q^35 - 91 * q^36 - 11 * q^37 - 58 * q^38 + 22 * q^39 - 136 * q^40 - 68 * q^41 - 114 * q^42 - 80 * q^43 - 138 * q^44 - 170 * q^45 - 132 * q^46 - 71 * q^47 - 276 * q^48 - 118 * q^49 - 284 * q^50 - 75 * q^51 - 308 * q^52 - 95 * q^53 - 438 * q^54 - 104 * q^55 - 189 * q^56 - 366 * q^57 - 322 * q^58 - 117 * q^59 - 348 * q^60 - 105 * q^61 - 332 * q^62 - 188 * q^63 - 391 * q^64 - 38 * q^65 - 414 * q^66 - 97 * q^67 - 328 * q^68 - 174 * q^69 - 218 * q^70 - 64 * q^71 - 379 * q^72 - 193 * q^73 - 312 * q^74 + 60 * q^75 - 288 * q^76 - 95 * q^77 - 376 * q^78 - 67 * q^79 - 104 * q^80 - 337 * q^81 - 100 * q^82 + 52 * q^83 - 138 * q^84 - 294 * q^85 - 18 * q^86 + 2 * q^87 + 50 * q^88 - 67 * q^89 + 212 * q^90 + 76 * q^91 + 142 * q^92 - 39 * q^93 + 274 * q^94 + 24 * q^95 + 152 * q^96 - 236 * q^97 + 135 * q^98 + 84 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(700))\)

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
700.2.a	\(\chi_{700}(1, \cdot)\)	700.2.a.a	1	1
		700.2.a.b	1
		700.2.a.c	1
		700.2.a.d	1
		700.2.a.e	1
		700.2.a.f	1
		700.2.a.g	1
		700.2.a.h	1
		700.2.a.i	1
		700.2.a.j	1
700.2.c	\(\chi_{700}(699, \cdot)\)	700.2.c.a	4	1
		700.2.c.b	4
		700.2.c.c	4
		700.2.c.d	4
		700.2.c.e	4
		700.2.c.f	4
		700.2.c.g	4
		700.2.c.h	8
		700.2.c.i	8
		700.2.c.j	8
		700.2.c.k	16
700.2.e	\(\chi_{700}(449, \cdot)\)	700.2.e.a	2	1
		700.2.e.b	2
		700.2.e.c	2
		700.2.e.d	2
700.2.g	\(\chi_{700}(251, \cdot)\)	700.2.g.a	2	1
		700.2.g.b	4
		700.2.g.c	4
		700.2.g.d	4
		700.2.g.e	4
		700.2.g.f	4
		700.2.g.g	4
		700.2.g.h	4
		700.2.g.i	8
		700.2.g.j	8
		700.2.g.k	8
		700.2.g.l	16
700.2.i	\(\chi_{700}(401, \cdot)\)	700.2.i.a	2	2
		700.2.i.b	2
		700.2.i.c	2
		700.2.i.d	6
		700.2.i.e	6
		700.2.i.f	8
700.2.k	\(\chi_{700}(43, \cdot)\)	700.2.k.a	24	2
		700.2.k.b	36
		700.2.k.c	48
700.2.m	\(\chi_{700}(293, \cdot)\)	700.2.m.a	8	2
		700.2.m.b	8
		700.2.m.c	8
700.2.n	\(\chi_{700}(141, \cdot)\)	700.2.n.a	4	4
		700.2.n.b	4
		700.2.n.c	20
		700.2.n.d	28
700.2.p	\(\chi_{700}(451, \cdot)\)	700.2.p.a	4	2
		700.2.p.b	8
		700.2.p.c	32
		700.2.p.d	32
		700.2.p.e	32
		700.2.p.f	32
700.2.r	\(\chi_{700}(149, \cdot)\)	700.2.r.a	4	2
		700.2.r.b	4
		700.2.r.c	4
		700.2.r.d	12
700.2.t	\(\chi_{700}(199, \cdot)\)	700.2.t.a	4	2
		700.2.t.b	4
		700.2.t.c	32
		700.2.t.d	32
		700.2.t.e	64
700.2.w	\(\chi_{700}(111, \cdot)\)	700.2.w.a	464	4
700.2.y	\(\chi_{700}(29, \cdot)\)	700.2.y.a	64	4
700.2.ba	\(\chi_{700}(139, \cdot)\)	700.2.ba.a	464	4
700.2.bc	\(\chi_{700}(157, \cdot)\)	700.2.bc.a	8	4
		700.2.bc.b	16
		700.2.bc.c	24
700.2.be	\(\chi_{700}(107, \cdot)\)	700.2.be.a	8	4
		700.2.be.b	8
		700.2.be.c	8
		700.2.be.d	48
		700.2.be.e	72
		700.2.be.f	128
700.2.bg	\(\chi_{700}(81, \cdot)\)	700.2.bg.a	160	8
700.2.bh	\(\chi_{700}(13, \cdot)\)	700.2.bh.a	160	8
700.2.bj	\(\chi_{700}(127, \cdot)\)	700.2.bj.a	720	8
700.2.bm	\(\chi_{700}(19, \cdot)\)	700.2.bm.a	928	8
700.2.bo	\(\chi_{700}(9, \cdot)\)	700.2.bo.a	160	8
700.2.bq	\(\chi_{700}(31, \cdot)\)	700.2.bq.a	928	8
700.2.bt	\(\chi_{700}(23, \cdot)\)	700.2.bt.a	1856	16
700.2.bv	\(\chi_{700}(17, \cdot)\)	700.2.bv.a	320	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(700))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(700)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 2}\)