Space of modular forms of level 2070 and weight 2

• Label: 2070.2
• Level: 2070
• Weight: 2
• Dimension: 27482
• Nonzero newspaces: 24
• Sturm bound: 456192
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(456192\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2070))\).

	Total	New	Old
Modular forms	116864	27482	89382
Cusp forms	111233	27482	83751
Eisenstein series	5631	0	5631

Trace form

27482 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 10 * q^5 + 12 * q^6 - 24 * q^7 + 6 * q^8 + 28 * q^9 + 22 * q^10 + 52 * q^11 + 16 * q^12 + 28 * q^13 + 40 * q^14 + 48 * q^15 - 6 * q^16 - 8 * q^17 + 8 * q^18 - 28 * q^19 + 72 * q^21 - 24 * q^22 - 52 * q^23 - 12 * q^24 - 10 * q^25 - 56 * q^26 + 48 * q^27 - 44 * q^28 - 32 * q^29 - 28 * q^31 - 6 * q^32 - 20 * q^33 - 8 * q^34 - 54 * q^35 - 20 * q^36 - 36 * q^37 - 84 * q^38 - 128 * q^39 + 6 * q^40 - 196 * q^41 - 128 * q^42 - 108 * q^43 - 64 * q^44 - 160 * q^45 - 208 * q^47 - 20 * q^48 - 138 * q^49 - 94 * q^50 - 60 * q^51 - 20 * q^52 - 104 * q^53 + 28 * q^54 + 128 * q^55 + 92 * q^56 + 212 * q^57 + 196 * q^58 + 464 * q^59 + 60 * q^60 + 500 * q^61 + 396 * q^62 + 520 * q^63 + 6 * q^64 + 546 * q^65 + 448 * q^66 + 300 * q^67 + 336 * q^68 + 504 * q^69 + 312 * q^70 + 804 * q^71 + 188 * q^72 + 380 * q^73 + 628 * q^74 + 296 * q^75 + 92 * q^76 + 684 * q^77 + 320 * q^78 + 548 * q^79 + 56 * q^80 + 348 * q^81 + 380 * q^82 + 280 * q^83 + 112 * q^84 + 170 * q^85 + 272 * q^86 + 40 * q^87 + 20 * q^88 + 48 * q^89 + 112 * q^90 + 40 * q^91 + 36 * q^92 - 64 * q^93 + 56 * q^94 - 2 * q^95 + 16 * q^96 + 176 * q^97 + 142 * q^98 + 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2070))\)

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
2070.2.a	\(\chi_{2070}(1, \cdot)\)	2070.2.a.a	1	1
		2070.2.a.b	1
		2070.2.a.c	1
		2070.2.a.d	1
		2070.2.a.e	1
		2070.2.a.f	1
		2070.2.a.g	1
		2070.2.a.h	1
		2070.2.a.i	1
		2070.2.a.j	1
		2070.2.a.k	1
		2070.2.a.l	1
		2070.2.a.m	1
		2070.2.a.n	1
		2070.2.a.o	1
		2070.2.a.p	1
		2070.2.a.q	1
		2070.2.a.r	1
		2070.2.a.s	1
		2070.2.a.t	2
		2070.2.a.u	2
		2070.2.a.v	2
		2070.2.a.w	2
		2070.2.a.x	2
		2070.2.a.y	2
		2070.2.a.z	3
2070.2.d	\(\chi_{2070}(829, \cdot)\)	2070.2.d.a	4	1
		2070.2.d.b	4
		2070.2.d.c	4
		2070.2.d.d	6
		2070.2.d.e	6
		2070.2.d.f	8
		2070.2.d.g	8
		2070.2.d.h	16
2070.2.e	\(\chi_{2070}(1241, \cdot)\)	2070.2.e.a	16	1
		2070.2.e.b	16
2070.2.h	\(\chi_{2070}(2069, \cdot)\)	2070.2.h.a	24	1
		2070.2.h.b	24
2070.2.i	\(\chi_{2070}(691, \cdot)\)	n/a	176	2
2070.2.j	\(\chi_{2070}(323, \cdot)\)	2070.2.j.a	4	2
		2070.2.j.b	4
		2070.2.j.c	4
		2070.2.j.d	4
		2070.2.j.e	4
		2070.2.j.f	4
		2070.2.j.g	12
		2070.2.j.h	16
		2070.2.j.i	16
		2070.2.j.j	20
2070.2.k	\(\chi_{2070}(1333, \cdot)\)	n/a	120	2
2070.2.n	\(\chi_{2070}(689, \cdot)\)	n/a	288	2
2070.2.q	\(\chi_{2070}(551, \cdot)\)	n/a	192	2
2070.2.r	\(\chi_{2070}(139, \cdot)\)	n/a	264	2
2070.2.u	\(\chi_{2070}(271, \cdot)\)	n/a	400	10
2070.2.x	\(\chi_{2070}(47, \cdot)\)	n/a	528	4
2070.2.y	\(\chi_{2070}(367, \cdot)\)	n/a	576	4
2070.2.z	\(\chi_{2070}(89, \cdot)\)	n/a	480	10
2070.2.bc	\(\chi_{2070}(251, \cdot)\)	n/a	320	10
2070.2.bd	\(\chi_{2070}(289, \cdot)\)	n/a	600	10
2070.2.bg	\(\chi_{2070}(31, \cdot)\)	n/a	1920	20
2070.2.bj	\(\chi_{2070}(37, \cdot)\)	n/a	1200	20
2070.2.bk	\(\chi_{2070}(197, \cdot)\)	n/a	960	20
2070.2.bn	\(\chi_{2070}(49, \cdot)\)	n/a	2880	20
2070.2.bo	\(\chi_{2070}(11, \cdot)\)	n/a	1920	20
2070.2.br	\(\chi_{2070}(149, \cdot)\)	n/a	2880	20
2070.2.bs	\(\chi_{2070}(7, \cdot)\)	n/a	5760	40
2070.2.bt	\(\chi_{2070}(77, \cdot)\)	n/a	5760	40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2070))\) into lower level spaces

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