Space of modular forms of level 700 and weight 4

• Label: 700.4
• Level: 700
• Weight: 4
• Dimension: 22054
• Nonzero newspaces: 24
• Sturm bound: 115200
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(115200\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(700))\).

	Total	New	Old
Modular forms	44040	22466	21574
Cusp forms	42360	22054	20306
Eisenstein series	1680	412	1268

Trace form

22054 * q - 27 * q^2 + 10 * q^3 - 19 * q^4 - 26 * q^5 + 8 * q^6 - 8 * q^7 - 183 * q^8 - 432 * q^9 - 176 * q^10 - 164 * q^11 - 504 * q^12 + 330 * q^13 - 185 * q^14 + 344 * q^15 + 625 * q^16 + 204 * q^17 + 1229 * q^18 + 62 * q^19 + 604 * q^20 + 206 * q^21 + 1514 * q^22 - 604 * q^23 + 312 * q^24 - 670 * q^25 - 1508 * q^26 - 716 * q^27 - 1141 * q^28 - 2052 * q^29 - 2508 * q^30 - 1088 * q^31 - 1707 * q^32 - 1692 * q^33 - 40 * q^34 - 596 * q^35 + 1449 * q^36 - 258 * q^37 - 216 * q^38 - 2040 * q^39 - 456 * q^40 + 2360 * q^41 - 410 * q^42 + 1540 * q^43 + 562 * q^44 + 7010 * q^45 - 2470 * q^46 + 6752 * q^47 + 1324 * q^48 + 2346 * q^49 + 4316 * q^50 + 1820 * q^51 + 2684 * q^52 - 358 * q^53 + 6912 * q^54 - 1904 * q^55 - 2837 * q^56 - 10996 * q^57 - 1970 * q^58 - 4258 * q^59 - 8188 * q^60 - 5854 * q^61 + 1852 * q^62 + 2168 * q^63 - 247 * q^64 - 1358 * q^65 + 1944 * q^66 + 5840 * q^67 + 1876 * q^68 + 3988 * q^69 + 9342 * q^70 + 5912 * q^71 + 8525 * q^72 + 14236 * q^73 + 10986 * q^74 - 3640 * q^75 + 11936 * q^76 + 1348 * q^77 + 17048 * q^78 - 7972 * q^79 - 264 * q^80 - 4348 * q^81 + 5500 * q^82 - 12426 * q^83 - 5150 * q^84 - 14954 * q^85 - 12410 * q^86 + 3364 * q^87 - 10414 * q^88 + 5386 * q^89 - 9628 * q^90 + 5942 * q^91 - 19378 * q^92 + 7312 * q^93 - 28876 * q^94 + 3064 * q^95 - 24856 * q^96 + 7896 * q^97 - 21421 * q^98 - 9676 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(700))\)

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
700.4.a	\(\chi_{700}(1, \cdot)\)	700.4.a.a	1	1
		700.4.a.b	1
		700.4.a.c	1
		700.4.a.d	1
		700.4.a.e	1
		700.4.a.f	1
		700.4.a.g	1
		700.4.a.h	1
		700.4.a.i	1
		700.4.a.j	1
		700.4.a.k	1
		700.4.a.l	1
		700.4.a.m	1
		700.4.a.n	1
		700.4.a.o	2
		700.4.a.p	2
		700.4.a.q	2
		700.4.a.r	2
		700.4.a.s	3
		700.4.a.t	3
700.4.c	\(\chi_{700}(699, \cdot)\)	n/a	212	1
700.4.e	\(\chi_{700}(449, \cdot)\)	700.4.e.a	2	1
		700.4.e.b	2
		700.4.e.c	2
		700.4.e.d	2
		700.4.e.e	2
		700.4.e.f	2
		700.4.e.g	2
		700.4.e.h	2
		700.4.e.i	2
		700.4.e.j	4
		700.4.e.k	6
700.4.g	\(\chi_{700}(251, \cdot)\)	n/a	222	1
700.4.i	\(\chi_{700}(401, \cdot)\)	700.4.i.a	2	2
		700.4.i.b	2
		700.4.i.c	2
		700.4.i.d	2
		700.4.i.e	4
		700.4.i.f	4
		700.4.i.g	4
		700.4.i.h	4
		700.4.i.i	14
		700.4.i.j	14
		700.4.i.k	24
700.4.k	\(\chi_{700}(43, \cdot)\)	n/a	324	2
700.4.m	\(\chi_{700}(293, \cdot)\)	700.4.m.a	8	2
		700.4.m.b	8
		700.4.m.c	24
		700.4.m.d	32
700.4.n	\(\chi_{700}(141, \cdot)\)	n/a	184	4
700.4.p	\(\chi_{700}(451, \cdot)\)	n/a	444	2
700.4.r	\(\chi_{700}(149, \cdot)\)	700.4.r.a	4	2
		700.4.r.b	4
		700.4.r.c	4
		700.4.r.d	8
		700.4.r.e	8
		700.4.r.f	8
		700.4.r.g	8
		700.4.r.h	28
700.4.t	\(\chi_{700}(199, \cdot)\)	n/a	424	2
700.4.w	\(\chi_{700}(111, \cdot)\)	n/a	1424	4
700.4.y	\(\chi_{700}(29, \cdot)\)	n/a	176	4
700.4.ba	\(\chi_{700}(139, \cdot)\)	n/a	1424	4
700.4.bc	\(\chi_{700}(157, \cdot)\)	n/a	144	4
700.4.be	\(\chi_{700}(107, \cdot)\)	n/a	848	4
700.4.bg	\(\chi_{700}(81, \cdot)\)	n/a	480	8
700.4.bh	\(\chi_{700}(13, \cdot)\)	n/a	480	8
700.4.bj	\(\chi_{700}(127, \cdot)\)	n/a	2160	8
700.4.bm	\(\chi_{700}(19, \cdot)\)	n/a	2848	8
700.4.bo	\(\chi_{700}(9, \cdot)\)	n/a	480	8
700.4.bq	\(\chi_{700}(31, \cdot)\)	n/a	2848	8
700.4.bt	\(\chi_{700}(23, \cdot)\)	n/a	5696	16
700.4.bv	\(\chi_{700}(17, \cdot)\)	n/a	960	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(700))\) into lower level spaces

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