Space of modular forms of level 1470 and weight 2

• Label: 1470.2
• Level: 1470
• Weight: 2
• Dimension: 12416
• Nonzero newspaces: 24
• Sturm bound: 225792
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(225792\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1470))\).

	Total	New	Old
Modular forms	58368	12416	45952
Cusp forms	54529	12416	42113
Eisenstein series	3839	0	3839

Trace form

12416 * q - 10 * q^3 - 16 * q^4 - 28 * q^5 - 26 * q^6 - 32 * q^7 - 32 * q^9 - 20 * q^10 - 80 * q^11 - 2 * q^12 - 48 * q^13 + 10 * q^15 - 24 * q^17 + 56 * q^18 - 48 * q^19 + 4 * q^20 + 20 * q^21 + 8 * q^22 - 24 * q^23 + 22 * q^24 + 40 * q^25 + 48 * q^26 + 134 * q^27 + 24 * q^28 + 120 * q^29 + 106 * q^30 + 48 * q^31 + 152 * q^33 + 112 * q^34 + 96 * q^35 + 64 * q^36 + 352 * q^37 + 240 * q^38 + 352 * q^39 + 72 * q^40 + 376 * q^41 + 180 * q^42 + 272 * q^43 + 176 * q^44 + 200 * q^45 + 456 * q^46 + 336 * q^47 + 26 * q^48 + 576 * q^49 + 80 * q^50 + 396 * q^51 + 104 * q^52 + 240 * q^53 + 70 * q^54 + 460 * q^55 + 144 * q^56 + 152 * q^57 + 400 * q^58 + 376 * q^59 + 60 * q^60 + 552 * q^61 + 96 * q^62 + 84 * q^63 - 16 * q^64 + 120 * q^65 + 24 * q^66 + 336 * q^67 - 24 * q^68 + 112 * q^69 - 56 * q^72 + 232 * q^73 - 104 * q^74 + 158 * q^75 - 32 * q^76 - 72 * q^77 - 84 * q^78 - 8 * q^79 - 28 * q^80 - 24 * q^81 - 256 * q^82 + 144 * q^83 - 52 * q^84 - 184 * q^86 + 44 * q^87 - 40 * q^88 + 80 * q^89 - 204 * q^90 + 112 * q^91 - 72 * q^92 + 104 * q^93 - 256 * q^94 + 144 * q^95 - 18 * q^96 + 48 * q^97 - 48 * q^98 - 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1470))\)

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
1470.2.a	\(\chi_{1470}(1, \cdot)\)	1470.2.a.a	1	1
		1470.2.a.b	1
		1470.2.a.c	1
		1470.2.a.d	1
		1470.2.a.e	1
		1470.2.a.f	1
		1470.2.a.g	1
		1470.2.a.h	1
		1470.2.a.i	1
		1470.2.a.j	1
		1470.2.a.k	1
		1470.2.a.l	1
		1470.2.a.m	1
		1470.2.a.n	1
		1470.2.a.o	1
		1470.2.a.p	1
		1470.2.a.q	1
		1470.2.a.r	1
		1470.2.a.s	2
		1470.2.a.t	2
		1470.2.a.u	2
		1470.2.a.v	2
1470.2.b	\(\chi_{1470}(881, \cdot)\)	1470.2.b.a	12	1
		1470.2.b.b	12
		1470.2.b.c	16
		1470.2.b.d	16
1470.2.d	\(\chi_{1470}(1469, \cdot)\)	1470.2.d.a	4	1
		1470.2.d.b	4
		1470.2.d.c	4
		1470.2.d.d	4
		1470.2.d.e	8
		1470.2.d.f	8
		1470.2.d.g	24
		1470.2.d.h	24
1470.2.g	\(\chi_{1470}(589, \cdot)\)	1470.2.g.a	2	1
		1470.2.g.b	2
		1470.2.g.c	2
		1470.2.g.d	2
		1470.2.g.e	2
		1470.2.g.f	2
		1470.2.g.g	2
		1470.2.g.h	6
		1470.2.g.i	6
		1470.2.g.j	8
		1470.2.g.k	8
1470.2.i	\(\chi_{1470}(361, \cdot)\)	1470.2.i.a	2	2
		1470.2.i.b	2
		1470.2.i.c	2
		1470.2.i.d	2
		1470.2.i.e	2
		1470.2.i.f	2
		1470.2.i.g	2
		1470.2.i.h	2
		1470.2.i.i	2
		1470.2.i.j	2
		1470.2.i.k	2
		1470.2.i.l	2
		1470.2.i.m	2
		1470.2.i.n	2
		1470.2.i.o	2
		1470.2.i.p	2
		1470.2.i.q	2
		1470.2.i.r	2
		1470.2.i.s	2
		1470.2.i.t	2
		1470.2.i.u	4
		1470.2.i.v	4
		1470.2.i.w	4
		1470.2.i.x	4
1470.2.j	\(\chi_{1470}(197, \cdot)\)	n/a	164	2
1470.2.m	\(\chi_{1470}(97, \cdot)\)	1470.2.m.a	8	2
		1470.2.m.b	8
		1470.2.m.c	16
		1470.2.m.d	16
		1470.2.m.e	16
		1470.2.m.f	16
1470.2.n	\(\chi_{1470}(79, \cdot)\)	1470.2.n.a	4	2
		1470.2.n.b	4
		1470.2.n.c	4
		1470.2.n.d	4
		1470.2.n.e	4
		1470.2.n.f	4
		1470.2.n.g	4
		1470.2.n.h	4
		1470.2.n.i	4
		1470.2.n.j	12
		1470.2.n.k	16
		1470.2.n.l	16
1470.2.r	\(\chi_{1470}(521, \cdot)\)	n/a	104	2
1470.2.t	\(\chi_{1470}(509, \cdot)\)	n/a	160	2
1470.2.u	\(\chi_{1470}(211, \cdot)\)	n/a	240	6
1470.2.v	\(\chi_{1470}(313, \cdot)\)	n/a	160	4
1470.2.y	\(\chi_{1470}(263, \cdot)\)	n/a	320	4
1470.2.bb	\(\chi_{1470}(169, \cdot)\)	n/a	336	6
1470.2.bc	\(\chi_{1470}(209, \cdot)\)	n/a	672	6
1470.2.be	\(\chi_{1470}(41, \cdot)\)	n/a	432	6
1470.2.bg	\(\chi_{1470}(121, \cdot)\)	n/a	432	12
1470.2.bi	\(\chi_{1470}(13, \cdot)\)	n/a	672	12
1470.2.bj	\(\chi_{1470}(113, \cdot)\)	n/a	1344	12
1470.2.bm	\(\chi_{1470}(59, \cdot)\)	n/a	1344	12
1470.2.bo	\(\chi_{1470}(101, \cdot)\)	n/a	912	12
1470.2.bq	\(\chi_{1470}(109, \cdot)\)	n/a	672	12
1470.2.bt	\(\chi_{1470}(23, \cdot)\)	n/a	2688	24
1470.2.bu	\(\chi_{1470}(73, \cdot)\)	n/a	1344	24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1470))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1470)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1470))\)\(^{\oplus 1}\)