Space of modular forms of level 1470 and weight 4

• Label: 1470.4
• Level: 1470
• Weight: 4
• Dimension: 37240
• Nonzero newspaces: 24
• Sturm bound: 451584
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(451584\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1470))\).

	Total	New	Old
Modular forms	171264	37240	134024
Cusp forms	167424	37240	130184
Eisenstein series	3840	0	3840

Trace form

37240 * q - 34 * q^3 + 100 * q^5 + 140 * q^6 + 192 * q^7 - 168 * q^9 - 184 * q^10 - 304 * q^11 - 200 * q^12 - 104 * q^13 + 266 * q^15 - 128 * q^16 - 24 * q^17 - 688 * q^18 - 1520 * q^19 - 16 * q^20 - 1296 * q^21 + 336 * q^22 + 408 * q^23 - 144 * q^24 + 4856 * q^25 + 2112 * q^26 + 2750 * q^27 + 192 * q^28 - 600 * q^29 - 588 * q^30 - 1200 * q^31 - 1960 * q^33 - 3488 * q^34 - 4020 * q^35 + 704 * q^36 + 8968 * q^37 + 5760 * q^38 + 1068 * q^39 + 1344 * q^40 + 2312 * q^41 - 72 * q^42 - 1016 * q^43 - 1664 * q^44 + 2632 * q^45 - 11824 * q^46 - 5328 * q^47 - 992 * q^48 - 24456 * q^49 - 3488 * q^50 - 1340 * q^51 + 1216 * q^52 - 4224 * q^53 + 828 * q^54 + 9712 * q^55 + 1152 * q^56 + 6152 * q^57 + 6720 * q^58 + 20456 * q^59 + 1664 * q^60 + 13040 * q^61 + 10656 * q^62 - 5460 * q^63 - 3072 * q^64 - 14448 * q^65 - 7888 * q^66 - 21848 * q^67 - 96 * q^68 - 7008 * q^69 + 1008 * q^70 + 672 * q^71 + 2752 * q^72 + 2176 * q^73 - 1936 * q^74 + 4306 * q^75 + 1024 * q^76 - 2088 * q^77 + 8616 * q^78 + 14056 * q^79 + 1600 * q^80 + 25912 * q^81 + 9216 * q^82 + 46608 * q^83 + 1824 * q^84 + 37288 * q^85 + 6160 * q^86 + 572 * q^87 - 1344 * q^88 + 4624 * q^89 - 12808 * q^90 - 16128 * q^91 + 8736 * q^92 - 38608 * q^93 + 10112 * q^94 - 22680 * q^95 + 448 * q^96 - 19976 * q^97 + 1632 * q^98 - 6744 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1470))\)

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
1470.4.a	\(\chi_{1470}(1, \cdot)\)	1470.4.a.a	1	1
		1470.4.a.b	1
		1470.4.a.c	1
		1470.4.a.d	1
		1470.4.a.e	1
		1470.4.a.f	1
		1470.4.a.g	1
		1470.4.a.h	1
		1470.4.a.i	1
		1470.4.a.j	1
		1470.4.a.k	1
		1470.4.a.l	1
		1470.4.a.m	1
		1470.4.a.n	1
		1470.4.a.o	1
		1470.4.a.p	1
		1470.4.a.q	1
		1470.4.a.r	1
		1470.4.a.s	1
		1470.4.a.t	1
		1470.4.a.u	1
		1470.4.a.v	1
		1470.4.a.w	1
		1470.4.a.x	1
		1470.4.a.y	1
		1470.4.a.z	1
		1470.4.a.ba	1
		1470.4.a.bb	1
		1470.4.a.bc	1
		1470.4.a.bd	1
		1470.4.a.be	2
		1470.4.a.bf	2
		1470.4.a.bg	2
		1470.4.a.bh	2
		1470.4.a.bi	2
		1470.4.a.bj	2
		1470.4.a.bk	2
		1470.4.a.bl	2
		1470.4.a.bm	2
		1470.4.a.bn	2
		1470.4.a.bo	2
		1470.4.a.bp	2
		1470.4.a.bq	2
		1470.4.a.br	2
		1470.4.a.bs	2
		1470.4.a.bt	3
		1470.4.a.bu	3
		1470.4.a.bv	4
		1470.4.a.bw	4
		1470.4.a.bx	4
		1470.4.a.by	4
1470.4.b	\(\chi_{1470}(881, \cdot)\)	n/a	160	1
1470.4.d	\(\chi_{1470}(1469, \cdot)\)	n/a	240	1
1470.4.g	\(\chi_{1470}(589, \cdot)\)	n/a	122	1
1470.4.i	\(\chi_{1470}(361, \cdot)\)	n/a	160	2
1470.4.j	\(\chi_{1470}(197, \cdot)\)	n/a	492	2
1470.4.m	\(\chi_{1470}(97, \cdot)\)	n/a	240	2
1470.4.n	\(\chi_{1470}(79, \cdot)\)	n/a	240	2
1470.4.r	\(\chi_{1470}(521, \cdot)\)	n/a	320	2
1470.4.t	\(\chi_{1470}(509, \cdot)\)	n/a	480	2
1470.4.u	\(\chi_{1470}(211, \cdot)\)	n/a	672	6
1470.4.v	\(\chi_{1470}(313, \cdot)\)	n/a	480	4
1470.4.y	\(\chi_{1470}(263, \cdot)\)	n/a	960	4
1470.4.bb	\(\chi_{1470}(169, \cdot)\)	n/a	1008	6
1470.4.bc	\(\chi_{1470}(209, \cdot)\)	n/a	2016	6
1470.4.be	\(\chi_{1470}(41, \cdot)\)	n/a	1344	6
1470.4.bg	\(\chi_{1470}(121, \cdot)\)	n/a	1344	12
1470.4.bi	\(\chi_{1470}(13, \cdot)\)	n/a	2016	12
1470.4.bj	\(\chi_{1470}(113, \cdot)\)	n/a	4032	12
1470.4.bm	\(\chi_{1470}(59, \cdot)\)	n/a	4032	12
1470.4.bo	\(\chi_{1470}(101, \cdot)\)	n/a	2688	12
1470.4.bq	\(\chi_{1470}(109, \cdot)\)	n/a	2016	12
1470.4.bt	\(\chi_{1470}(23, \cdot)\)	n/a	8064	24
1470.4.bu	\(\chi_{1470}(73, \cdot)\)	n/a	4032	24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1470))\) into lower level spaces

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