Space of modular forms of level 2070 and weight 4

• Label: 2070.4
• Level: 2070
• Weight: 4
• Dimension: 82450
• Nonzero newspaces: 24
• Sturm bound: 912384
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(912384\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2070))\).

	Total	New	Old
Modular forms	344960	82450	262510
Cusp forms	339328	82450	256878
Eisenstein series	5632	0	5632

Trace form

82450 * q + 12 * q^2 + 12 * q^3 - 24 * q^4 + 34 * q^5 - 72 * q^6 - 8 * q^7 - 48 * q^8 - 164 * q^9 + 68 * q^10 + 68 * q^11 - 32 * q^12 - 596 * q^13 - 400 * q^14 - 492 * q^15 - 224 * q^16 - 1060 * q^17 + 560 * q^18 + 1704 * q^19 + 840 * q^20 + 1440 * q^21 + 2096 * q^22 + 2284 * q^23 - 96 * q^24 + 262 * q^25 - 688 * q^26 - 1104 * q^27 - 960 * q^28 - 4636 * q^29 - 576 * q^30 - 4096 * q^31 + 192 * q^32 - 572 * q^33 + 1648 * q^34 - 1686 * q^35 + 1168 * q^36 + 2356 * q^37 + 1944 * q^38 + 1864 * q^39 - 240 * q^40 + 5356 * q^41 + 1600 * q^42 + 988 * q^43 - 1280 * q^44 + 5636 * q^45 - 1712 * q^46 + 8080 * q^47 + 448 * q^48 + 3750 * q^49 + 1468 * q^50 + 60 * q^51 + 880 * q^52 - 2392 * q^53 + 11896 * q^54 + 13564 * q^55 + 10528 * q^56 + 8396 * q^57 + 14424 * q^58 + 2992 * q^59 + 480 * q^60 + 4796 * q^61 - 10392 * q^62 - 21512 * q^63 + 1920 * q^64 - 23736 * q^65 - 20864 * q^66 - 7988 * q^67 - 18912 * q^68 - 29148 * q^69 - 24480 * q^70 - 56856 * q^71 - 9952 * q^72 - 15908 * q^73 - 24424 * q^74 - 17488 * q^75 - 8816 * q^76 - 15360 * q^77 + 1376 * q^78 + 3516 * q^79 + 3040 * q^80 + 29292 * q^81 + 17544 * q^82 + 61652 * q^83 + 18880 * q^84 + 25490 * q^85 + 46384 * q^86 + 16720 * q^87 + 4512 * q^88 + 36648 * q^89 + 13888 * q^90 + 43656 * q^91 + 1392 * q^92 + 11672 * q^93 + 6608 * q^94 + 20096 * q^95 + 1024 * q^96 + 21636 * q^97 + 13028 * q^98 - 5024 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2070))\)

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
2070.4.a	\(\chi_{2070}(1, \cdot)\)	2070.4.a.a	1	1
		2070.4.a.b	1
		2070.4.a.c	1
		2070.4.a.d	1
		2070.4.a.e	1
		2070.4.a.f	1
		2070.4.a.g	1
		2070.4.a.h	1
		2070.4.a.i	1
		2070.4.a.j	1
		2070.4.a.k	1
		2070.4.a.l	1
		2070.4.a.m	1
		2070.4.a.n	1
		2070.4.a.o	1
		2070.4.a.p	2
		2070.4.a.q	2
		2070.4.a.r	2
		2070.4.a.s	2
		2070.4.a.t	2
		2070.4.a.u	3
		2070.4.a.v	3
		2070.4.a.w	3
		2070.4.a.x	3
		2070.4.a.y	3
		2070.4.a.z	3
		2070.4.a.ba	3
		2070.4.a.bb	3
		2070.4.a.bc	3
		2070.4.a.bd	3
		2070.4.a.be	3
		2070.4.a.bf	4
		2070.4.a.bg	4
		2070.4.a.bh	4
		2070.4.a.bi	4
		2070.4.a.bj	4
		2070.4.a.bk	5
		2070.4.a.bl	5
		2070.4.a.bm	5
		2070.4.a.bn	5
		2070.4.a.bo	6
		2070.4.a.bp	6
2070.4.d	\(\chi_{2070}(829, \cdot)\)	n/a	164	1
2070.4.e	\(\chi_{2070}(1241, \cdot)\)	2070.4.e.a	48	1
		2070.4.e.b	48
2070.4.h	\(\chi_{2070}(2069, \cdot)\)	n/a	144	1
2070.4.i	\(\chi_{2070}(691, \cdot)\)	n/a	528	2
2070.4.j	\(\chi_{2070}(323, \cdot)\)	n/a	264	2
2070.4.k	\(\chi_{2070}(1333, \cdot)\)	n/a	360	2
2070.4.n	\(\chi_{2070}(689, \cdot)\)	n/a	864	2
2070.4.q	\(\chi_{2070}(551, \cdot)\)	n/a	576	2
2070.4.r	\(\chi_{2070}(139, \cdot)\)	n/a	792	2
2070.4.u	\(\chi_{2070}(271, \cdot)\)	n/a	1200	10
2070.4.x	\(\chi_{2070}(47, \cdot)\)	n/a	1584	4
2070.4.y	\(\chi_{2070}(367, \cdot)\)	n/a	1728	4
2070.4.z	\(\chi_{2070}(89, \cdot)\)	n/a	1440	10
2070.4.bc	\(\chi_{2070}(251, \cdot)\)	n/a	960	10
2070.4.bd	\(\chi_{2070}(289, \cdot)\)	n/a	1800	10
2070.4.bg	\(\chi_{2070}(31, \cdot)\)	n/a	5760	20
2070.4.bj	\(\chi_{2070}(37, \cdot)\)	n/a	3600	20
2070.4.bk	\(\chi_{2070}(197, \cdot)\)	n/a	2880	20
2070.4.bn	\(\chi_{2070}(49, \cdot)\)	n/a	8640	20
2070.4.bo	\(\chi_{2070}(11, \cdot)\)	n/a	5760	20
2070.4.br	\(\chi_{2070}(149, \cdot)\)	n/a	8640	20
2070.4.bs	\(\chi_{2070}(7, \cdot)\)	n/a	17280	40
2070.4.bt	\(\chi_{2070}(77, \cdot)\)	n/a	17280	40

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2070))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2070)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1035))\)\(^{\oplus 2}\)