Space of modular forms of level 1870 and weight 4

• Label: 1870.4
• Level: 1870
• Weight: 4
• Dimension: 92808
• Nonzero newspaces: 36
• Sturm bound: 829440
• Trace bound: 28

Defining parameters

Level:	\( N \)	=	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(829440\)
Trace bound:			\(28\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1870))\).

	Total	New	Old
Modular forms	313600	92808	220792
Cusp forms	308480	92808	215672
Eisenstein series	5120	0	5120

Trace form

92808 * q + 8 * q^2 - 32 * q^3 - 16 * q^4 - 20 * q^5 + 168 * q^6 + 64 * q^7 + 32 * q^8 - 308 * q^9 + 208 * q^10 - 40 * q^11 - 320 * q^12 - 648 * q^13 - 1008 * q^14 - 844 * q^15 - 64 * q^16 - 272 * q^17 - 576 * q^18 - 1460 * q^19 + 208 * q^20 - 368 * q^21 + 496 * q^22 + 3752 * q^23 + 1696 * q^24 + 3452 * q^25 + 1712 * q^26 + 844 * q^27 - 544 * q^28 - 3120 * q^29 - 2040 * q^30 - 3512 * q^31 - 512 * q^32 - 7364 * q^33 - 424 * q^34 - 2004 * q^35 - 544 * q^36 - 3784 * q^37 + 2352 * q^38 + 11136 * q^39 + 13024 * q^41 + 5040 * q^42 + 4648 * q^43 - 208 * q^44 - 3600 * q^45 - 5152 * q^46 - 14456 * q^47 - 512 * q^48 - 11980 * q^49 + 1080 * q^50 - 9038 * q^51 - 3232 * q^52 + 5432 * q^53 + 1088 * q^54 + 16724 * q^55 + 1536 * q^56 + 13596 * q^57 + 6768 * q^58 + 8652 * q^59 + 5440 * q^60 + 18904 * q^61 + 22160 * q^62 + 10416 * q^63 - 256 * q^64 - 4288 * q^65 + 1408 * q^66 - 29584 * q^67 - 5120 * q^68 - 56544 * q^69 - 35472 * q^70 - 36320 * q^71 - 9056 * q^72 - 17984 * q^73 - 13392 * q^74 - 13900 * q^75 - 6560 * q^76 + 6744 * q^77 + 2624 * q^78 + 24064 * q^79 + 4544 * q^80 + 43280 * q^81 + 24472 * q^82 + 52596 * q^83 + 16960 * q^84 + 61760 * q^85 + 26344 * q^86 + 67360 * q^87 + 7040 * q^88 + 31408 * q^89 + 33072 * q^90 + 18536 * q^91 - 2816 * q^92 - 23416 * q^93 - 13184 * q^94 - 44384 * q^95 - 512 * q^96 - 49036 * q^97 - 34368 * q^98 - 50320 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1870))\)

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
1870.4.a	\(\chi_{1870}(1, \cdot)\)	1870.4.a.a	1	1
		1870.4.a.b	1
		1870.4.a.c	8
		1870.4.a.d	8
		1870.4.a.e	9
		1870.4.a.f	9
		1870.4.a.g	9
		1870.4.a.h	9
		1870.4.a.i	10
		1870.4.a.j	10
		1870.4.a.k	10
		1870.4.a.l	10
		1870.4.a.m	10
		1870.4.a.n	11
		1870.4.a.o	11
		1870.4.a.p	11
		1870.4.a.q	11
		1870.4.a.r	12
1870.4.b	\(\chi_{1870}(749, \cdot)\)	n/a	240	1
1870.4.c	\(\chi_{1870}(441, \cdot)\)	n/a	180	1
1870.4.h	\(\chi_{1870}(1189, \cdot)\)	n/a	268	1
1870.4.j	\(\chi_{1870}(1033, \cdot)\)	n/a	648	2
1870.4.k	\(\chi_{1870}(89, \cdot)\)	n/a	536	2
1870.4.o	\(\chi_{1870}(373, \cdot)\)	n/a	648	2
1870.4.p	\(\chi_{1870}(307, \cdot)\)	n/a	576	2
1870.4.q	\(\chi_{1870}(1101, \cdot)\)	n/a	360	2
1870.4.s	\(\chi_{1870}(1143, \cdot)\)	n/a	648	2
1870.4.u	\(\chi_{1870}(511, \cdot)\)	n/a	768	4
1870.4.v	\(\chi_{1870}(111, \cdot)\)	n/a	720	4
1870.4.z	\(\chi_{1870}(417, \cdot)\)	n/a	1296	4
1870.4.ba	\(\chi_{1870}(43, \cdot)\)	n/a	1296	4
1870.4.bb	\(\chi_{1870}(529, \cdot)\)	n/a	1088	4
1870.4.bd	\(\chi_{1870}(169, \cdot)\)	n/a	1296	4
1870.4.bi	\(\chi_{1870}(951, \cdot)\)	n/a	864	4
1870.4.bj	\(\chi_{1870}(69, \cdot)\)	n/a	1152	4
1870.4.bl	\(\chi_{1870}(133, \cdot)\)	n/a	2160	8
1870.4.bn	\(\chi_{1870}(131, \cdot)\)	n/a	1728	8
1870.4.bp	\(\chi_{1870}(109, \cdot)\)	n/a	2592	8
1870.4.bq	\(\chi_{1870}(23, \cdot)\)	n/a	2160	8
1870.4.bt	\(\chi_{1870}(123, \cdot)\)	n/a	2592	8
1870.4.bv	\(\chi_{1870}(81, \cdot)\)	n/a	1728	8
1870.4.bw	\(\chi_{1870}(613, \cdot)\)	n/a	2304	8
1870.4.bx	\(\chi_{1870}(237, \cdot)\)	n/a	2592	8
1870.4.cb	\(\chi_{1870}(489, \cdot)\)	n/a	2592	8
1870.4.cc	\(\chi_{1870}(13, \cdot)\)	n/a	2592	8
1870.4.ce	\(\chi_{1870}(9, \cdot)\)	n/a	5184	16
1870.4.ci	\(\chi_{1870}(83, \cdot)\)	n/a	5184	16
1870.4.cj	\(\chi_{1870}(117, \cdot)\)	n/a	5184	16
1870.4.ck	\(\chi_{1870}(291, \cdot)\)	n/a	3456	16
1870.4.cn	\(\chi_{1870}(37, \cdot)\)	n/a	10368	32
1870.4.co	\(\chi_{1870}(41, \cdot)\)	n/a	6912	32
1870.4.cq	\(\chi_{1870}(29, \cdot)\)	n/a	10368	32
1870.4.cs	\(\chi_{1870}(3, \cdot)\)	n/a	10368	32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1870))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1870)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(374))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(935))\)\(^{\oplus 2}\)