Space of modular forms of level 1530 and weight 2

• Label: 1530.2
• Level: 1530
• Weight: 2
• Dimension: 14942
• Nonzero newspaces: 36
• Sturm bound: 248832
• Trace bound: 27

Defining parameters

Level:	\( N \)	=	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(248832\)
Trace bound:			\(27\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1530))\).

	Total	New	Old
Modular forms	64256	14942	49314
Cusp forms	60161	14942	45219
Eisenstein series	4095	0	4095

Trace form

14942 * 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 + 18 * q^10 + 20 * q^11 + 16 * q^12 - 4 * q^13 + 8 * q^14 + 48 * q^15 - 14 * q^16 - 14 * q^17 + 8 * q^18 - 16 * q^19 + 18 * q^20 + 72 * q^21 - 12 * q^22 + 40 * q^23 - 12 * q^24 - 2 * q^25 - 20 * q^26 + 48 * q^27 - 28 * q^29 - 48 * q^31 - 6 * q^32 - 20 * q^33 - 4 * q^34 - 64 * q^35 - 20 * q^36 - 12 * q^37 - 36 * q^38 + 6 * q^40 + 96 * q^41 + 64 * q^42 + 124 * q^43 + 128 * q^44 - 32 * q^45 + 192 * q^46 + 360 * q^47 - 20 * q^48 + 378 * q^49 - 46 * q^50 + 226 * q^51 + 172 * q^52 + 316 * q^53 + 164 * q^54 + 216 * q^55 - 40 * q^56 + 268 * q^57 + 124 * q^58 + 332 * q^59 + 80 * q^60 + 132 * q^61 + 288 * q^62 + 272 * q^63 + 6 * q^64 + 176 * q^65 + 128 * q^66 + 4 * q^67 + 44 * q^68 + 128 * q^69 + 144 * q^70 + 176 * q^71 + 12 * q^72 + 268 * q^73 + 172 * q^74 - 12 * q^75 + 92 * q^76 + 120 * q^77 + 56 * q^78 + 160 * q^79 + 38 * q^80 - 4 * q^81 + 252 * q^82 + 40 * q^83 + 24 * q^84 + 410 * q^85 + 204 * q^86 + 232 * q^87 + 84 * q^88 + 476 * q^89 + 112 * q^90 + 704 * q^91 + 104 * q^92 + 192 * q^93 + 184 * q^94 + 408 * q^95 + 16 * q^96 + 408 * q^97 + 126 * q^98 + 328 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1530))\)

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
1530.2.a	\(\chi_{1530}(1, \cdot)\)	1530.2.a.a	1	1
		1530.2.a.b	1
		1530.2.a.c	1
		1530.2.a.d	1
		1530.2.a.e	1
		1530.2.a.f	1
		1530.2.a.g	1
		1530.2.a.h	1
		1530.2.a.i	1
		1530.2.a.j	1
		1530.2.a.k	1
		1530.2.a.l	1
		1530.2.a.m	1
		1530.2.a.n	1
		1530.2.a.o	1
		1530.2.a.p	1
		1530.2.a.q	2
		1530.2.a.r	2
		1530.2.a.s	2
		1530.2.a.t	2
1530.2.c	\(\chi_{1530}(271, \cdot)\)	1530.2.c.a	2	1
		1530.2.c.b	2
		1530.2.c.c	2
		1530.2.c.d	2
		1530.2.c.e	2
		1530.2.c.f	4
		1530.2.c.g	4
		1530.2.c.h	6
		1530.2.c.i	6
1530.2.d	\(\chi_{1530}(919, \cdot)\)	1530.2.d.a	2	1
		1530.2.d.b	2
		1530.2.d.c	2
		1530.2.d.d	2
		1530.2.d.e	4
		1530.2.d.f	4
		1530.2.d.g	6
		1530.2.d.h	6
		1530.2.d.i	6
		1530.2.d.j	6
1530.2.f	\(\chi_{1530}(1189, \cdot)\)	1530.2.f.a	2	1
		1530.2.f.b	2
		1530.2.f.c	2
		1530.2.f.d	2
		1530.2.f.e	2
		1530.2.f.f	2
		1530.2.f.g	4
		1530.2.f.h	4
		1530.2.f.i	4
		1530.2.f.j	6
		1530.2.f.k	6
		1530.2.f.l	8
1530.2.i	\(\chi_{1530}(511, \cdot)\)	n/a	128	2
1530.2.j	\(\chi_{1530}(863, \cdot)\)	1530.2.j.a	4	2
		1530.2.j.b	28
		1530.2.j.c	40
1530.2.m	\(\chi_{1530}(647, \cdot)\)	1530.2.m.a	4	2
		1530.2.m.b	4
		1530.2.m.c	4
		1530.2.m.d	4
		1530.2.m.e	4
		1530.2.m.f	4
		1530.2.m.g	8
		1530.2.m.h	16
		1530.2.m.i	16
1530.2.n	\(\chi_{1530}(829, \cdot)\)	1530.2.n.a	2	2
		1530.2.n.b	2
		1530.2.n.c	2
		1530.2.n.d	2
		1530.2.n.e	2
		1530.2.n.f	2
		1530.2.n.g	2
		1530.2.n.h	2
		1530.2.n.i	4
		1530.2.n.j	4
		1530.2.n.k	4
		1530.2.n.l	4
		1530.2.n.m	4
		1530.2.n.n	4
		1530.2.n.o	4
		1530.2.n.p	4
		1530.2.n.q	8
		1530.2.n.r	8
		1530.2.n.s	12
		1530.2.n.t	12
1530.2.q	\(\chi_{1530}(361, \cdot)\)	1530.2.q.a	4	2
		1530.2.q.b	4
		1530.2.q.c	4
		1530.2.q.d	4
		1530.2.q.e	4
		1530.2.q.f	8
		1530.2.q.g	8
		1530.2.q.h	8
		1530.2.q.i	8
		1530.2.q.j	8
1530.2.r	\(\chi_{1530}(917, \cdot)\)	1530.2.r.a	4	2
		1530.2.r.b	4
		1530.2.r.c	24
		1530.2.r.d	40
1530.2.u	\(\chi_{1530}(557, \cdot)\)	1530.2.u.a	4	2
		1530.2.u.b	28
		1530.2.u.c	40
1530.2.x	\(\chi_{1530}(169, \cdot)\)	n/a	216	2
1530.2.z	\(\chi_{1530}(409, \cdot)\)	n/a	192	2
1530.2.ba	\(\chi_{1530}(781, \cdot)\)	n/a	144	2
1530.2.bc	\(\chi_{1530}(451, \cdot)\)	n/a	120	4
1530.2.be	\(\chi_{1530}(287, \cdot)\)	n/a	144	4
1530.2.bh	\(\chi_{1530}(53, \cdot)\)	n/a	144	4
1530.2.bj	\(\chi_{1530}(19, \cdot)\)	n/a	184	4
1530.2.bk	\(\chi_{1530}(47, \cdot)\)	n/a	432	4
1530.2.bn	\(\chi_{1530}(203, \cdot)\)	n/a	432	4
1530.2.bo	\(\chi_{1530}(421, \cdot)\)	n/a	288	4
1530.2.br	\(\chi_{1530}(259, \cdot)\)	n/a	432	4
1530.2.bs	\(\chi_{1530}(137, \cdot)\)	n/a	384	4
1530.2.bv	\(\chi_{1530}(353, \cdot)\)	n/a	432	4
1530.2.bx	\(\chi_{1530}(73, \cdot)\)	n/a	360	8
1530.2.bz	\(\chi_{1530}(71, \cdot)\)	n/a	192	8
1530.2.cb	\(\chi_{1530}(269, \cdot)\)	n/a	288	8
1530.2.cc	\(\chi_{1530}(37, \cdot)\)	n/a	360	8
1530.2.ce	\(\chi_{1530}(49, \cdot)\)	n/a	864	8
1530.2.ch	\(\chi_{1530}(77, \cdot)\)	n/a	864	8
1530.2.ci	\(\chi_{1530}(257, \cdot)\)	n/a	864	8
1530.2.cl	\(\chi_{1530}(121, \cdot)\)	n/a	576	8
1530.2.cn	\(\chi_{1530}(97, \cdot)\)	n/a	1728	16
1530.2.co	\(\chi_{1530}(29, \cdot)\)	n/a	1728	16
1530.2.cq	\(\chi_{1530}(11, \cdot)\)	n/a	1152	16
1530.2.cs	\(\chi_{1530}(7, \cdot)\)	n/a	1728	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1530))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1530)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(765))\)\(^{\oplus 2}\)