Space of modular forms of level 700 and weight 5

• Label: 700.5
• Level: 700
• Weight: 5
• Dimension: 29472
• Nonzero newspaces: 24
• Sturm bound: 144000
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(144000\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(700))\).

	Total	New	Old
Modular forms	58440	29880	28560
Cusp forms	56760	29472	27288
Eisenstein series	1680	408	1272

Trace form

29472 * q - 19 * q^2 - 31 * q^3 - 67 * q^4 - 76 * q^5 + 98 * q^6 + 272 * q^7 + 287 * q^8 - 76 * q^9 - 336 * q^10 - 1029 * q^11 - 474 * q^12 - 1504 * q^13 - 721 * q^14 + 1084 * q^15 - 1687 * q^16 + 2335 * q^17 - 1401 * q^18 + 1853 * q^19 - 276 * q^20 - 1405 * q^21 + 2716 * q^22 + 279 * q^23 + 11002 * q^24 - 4320 * q^25 + 6128 * q^26 + 2900 * q^27 + 1371 * q^28 + 2904 * q^29 - 1868 * q^30 - 4707 * q^31 - 14749 * q^32 - 1981 * q^33 - 20170 * q^34 + 564 * q^35 - 19263 * q^36 - 8011 * q^37 + 17816 * q^38 - 5788 * q^39 + 11064 * q^40 + 5984 * q^41 + 860 * q^42 - 19048 * q^43 - 8224 * q^44 - 30720 * q^45 + 17726 * q^46 - 9747 * q^47 - 9902 * q^48 - 6136 * q^49 + 2716 * q^50 + 36181 * q^51 - 20472 * q^52 + 68845 * q^53 + 35474 * q^54 + 50856 * q^55 + 47857 * q^56 + 55582 * q^57 + 28334 * q^58 - 37923 * q^59 - 21708 * q^60 - 44649 * q^61 - 40852 * q^62 - 99554 * q^63 - 47743 * q^64 - 9988 * q^65 + 46010 * q^66 - 15001 * q^67 + 24146 * q^68 - 13376 * q^69 + 14182 * q^70 + 30432 * q^71 - 70861 * q^72 + 13879 * q^73 - 103580 * q^74 + 19260 * q^75 + 7570 * q^76 + 77657 * q^77 + 75216 * q^78 + 42423 * q^79 + 77376 * q^80 + 114233 * q^81 - 20750 * q^82 - 10020 * q^83 - 42136 * q^84 + 9336 * q^85 + 61220 * q^86 - 166446 * q^87 + 186880 * q^88 - 79149 * q^89 + 202532 * q^90 - 15588 * q^91 + 63020 * q^92 - 125729 * q^93 + 61902 * q^94 + 7344 * q^95 - 165910 * q^96 - 60768 * q^97 - 74245 * q^98 + 175368 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(700))\)

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
700.5.b	\(\chi_{700}(351, \cdot)\)	n/a	228	1
700.5.d	\(\chi_{700}(601, \cdot)\)	700.5.d.a	2	1
		700.5.d.b	4
		700.5.d.c	10
		700.5.d.d	10
		700.5.d.e	12
		700.5.d.f	12
700.5.f	\(\chi_{700}(99, \cdot)\)	n/a	216	1
700.5.h	\(\chi_{700}(349, \cdot)\)	700.5.h.a	4	1
		700.5.h.b	20
		700.5.h.c	24
700.5.j	\(\chi_{700}(307, \cdot)\)	n/a	568	2
700.5.l	\(\chi_{700}(57, \cdot)\)	700.5.l.a	16	2
		700.5.l.b	24
		700.5.l.c	32
700.5.o	\(\chi_{700}(549, \cdot)\)	700.5.o.a	12	2
		700.5.o.b	40
		700.5.o.c	44
700.5.q	\(\chi_{700}(499, \cdot)\)	n/a	568	2
700.5.s	\(\chi_{700}(101, \cdot)\)	700.5.s.a	6	2
		700.5.s.b	20
		700.5.s.c	22
		700.5.s.d	22
		700.5.s.e	32
700.5.u	\(\chi_{700}(51, \cdot)\)	n/a	596	2
700.5.v	\(\chi_{700}(69, \cdot)\)	n/a	320	4
700.5.x	\(\chi_{700}(239, \cdot)\)	n/a	1440	4
700.5.z	\(\chi_{700}(41, \cdot)\)	n/a	320	4
700.5.bb	\(\chi_{700}(71, \cdot)\)	n/a	1440	4
700.5.bd	\(\chi_{700}(93, \cdot)\)	n/a	192	4
700.5.bf	\(\chi_{700}(143, \cdot)\)	n/a	1136	4
700.5.bi	\(\chi_{700}(113, \cdot)\)	n/a	480	8
700.5.bk	\(\chi_{700}(27, \cdot)\)	n/a	3808	8
700.5.bl	\(\chi_{700}(11, \cdot)\)	n/a	3808	8
700.5.bn	\(\chi_{700}(61, \cdot)\)	n/a	640	8
700.5.bp	\(\chi_{700}(39, \cdot)\)	n/a	3808	8
700.5.br	\(\chi_{700}(89, \cdot)\)	n/a	640	8
700.5.bs	\(\chi_{700}(3, \cdot)\)	n/a	7616	16
700.5.bu	\(\chi_{700}(37, \cdot)\)	n/a	1280	16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(700))\) into lower level spaces

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