Space of modular forms of level 3150 and weight 2

• Label: 3150.2
• Level: 3150
• Weight: 2
• Dimension: 60416
• Nonzero newspaces: 60
• Sturm bound: 1036800
• Trace bound: 16

Defining parameters

Level:	\( N \)	=	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(1036800\)
Trace bound:			\(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3150))\).

	Total	New	Old
Modular forms	264576	60416	204160
Cusp forms	253825	60416	193409
Eisenstein series	10751	0	10751

Trace form

60416 * q + 6 * q^2 + 6 * q^3 + 8 * q^4 + 10 * q^5 - 6 * q^6 + 26 * q^7 - 38 * q^9 - 22 * q^10 - 74 * q^11 - 32 * q^12 - 66 * q^13 - 64 * q^14 - 48 * q^15 - 196 * q^17 - 76 * q^18 - 158 * q^19 - 32 * q^20 - 90 * q^21 - 138 * q^22 - 236 * q^23 - 6 * q^24 - 158 * q^25 - 70 * q^26 - 132 * q^27 - 56 * q^28 - 260 * q^29 - 188 * q^31 - 4 * q^32 - 38 * q^33 - 100 * q^34 - 76 * q^35 + 58 * q^36 - 314 * q^37 + 96 * q^38 + 220 * q^39 - 6 * q^40 + 66 * q^41 + 128 * q^42 - 126 * q^43 + 56 * q^44 + 160 * q^45 - 96 * q^46 + 112 * q^47 + 58 * q^48 - 34 * q^49 + 114 * q^50 + 210 * q^51 + 18 * q^52 + 246 * q^53 + 246 * q^54 - 144 * q^55 + 40 * q^56 + 218 * q^57 + 76 * q^58 + 80 * q^59 + 64 * q^60 + 42 * q^61 + 396 * q^62 + 252 * q^63 + 2 * q^64 + 434 * q^65 + 144 * q^66 + 150 * q^67 + 294 * q^68 + 412 * q^69 + 216 * q^70 + 24 * q^71 - 6 * q^72 + 208 * q^73 + 496 * q^74 + 592 * q^75 + 64 * q^76 + 402 * q^77 + 300 * q^78 + 196 * q^79 + 10 * q^80 + 262 * q^81 + 392 * q^82 + 782 * q^83 + 78 * q^84 + 322 * q^85 + 242 * q^86 + 644 * q^87 + 110 * q^88 + 1138 * q^89 + 320 * q^90 + 494 * q^91 + 276 * q^92 + 772 * q^93 + 464 * q^94 + 520 * q^95 + 52 * q^96 + 554 * q^97 + 696 * q^98 + 676 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3150))\)

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
3150.2.a	\(\chi_{3150}(1, \cdot)\)	3150.2.a.a	1	1
		3150.2.a.b	1
		3150.2.a.c	1
		3150.2.a.d	1
		3150.2.a.e	1
		3150.2.a.f	1
		3150.2.a.g	1
		3150.2.a.h	1
		3150.2.a.i	1
		3150.2.a.j	1
		3150.2.a.k	1
		3150.2.a.l	1
		3150.2.a.m	1
		3150.2.a.n	1
		3150.2.a.o	1
		3150.2.a.p	1
		3150.2.a.q	1
		3150.2.a.r	1
		3150.2.a.s	1
		3150.2.a.t	1
		3150.2.a.u	1
		3150.2.a.v	1
		3150.2.a.w	1
		3150.2.a.x	1
		3150.2.a.y	1
		3150.2.a.z	1
		3150.2.a.ba	1
		3150.2.a.bb	1
		3150.2.a.bc	1
		3150.2.a.bd	1
		3150.2.a.be	1
		3150.2.a.bf	1
		3150.2.a.bg	1
		3150.2.a.bh	1
		3150.2.a.bi	1
		3150.2.a.bj	1
		3150.2.a.bk	1
		3150.2.a.bl	1
		3150.2.a.bm	1
		3150.2.a.bn	1
		3150.2.a.bo	1
		3150.2.a.bp	1
		3150.2.a.bq	1
		3150.2.a.br	1
		3150.2.a.bs	2
		3150.2.a.bt	2
3150.2.b	\(\chi_{3150}(251, \cdot)\)	3150.2.b.a	8	1
		3150.2.b.b	8
		3150.2.b.c	8
		3150.2.b.d	8
		3150.2.b.e	8
		3150.2.b.f	8
3150.2.d	\(\chi_{3150}(3149, \cdot)\)	3150.2.d.a	8	1
		3150.2.d.b	8
		3150.2.d.c	8
		3150.2.d.d	8
		3150.2.d.e	8
		3150.2.d.f	8
3150.2.g	\(\chi_{3150}(2899, \cdot)\)	3150.2.g.a	2	1
		3150.2.g.b	2
		3150.2.g.c	2
		3150.2.g.d	2
		3150.2.g.e	2
		3150.2.g.f	2
		3150.2.g.g	2
		3150.2.g.h	2
		3150.2.g.i	2
		3150.2.g.j	2
		3150.2.g.k	2
		3150.2.g.l	2
		3150.2.g.m	2
		3150.2.g.n	2
		3150.2.g.o	2
		3150.2.g.p	2
		3150.2.g.q	2
		3150.2.g.r	2
		3150.2.g.s	2
		3150.2.g.t	2
		3150.2.g.u	2
		3150.2.g.v	2
3150.2.i	\(\chi_{3150}(151, \cdot)\)	n/a	304	2
3150.2.j	\(\chi_{3150}(1051, \cdot)\)	n/a	228	2
3150.2.k	\(\chi_{3150}(1801, \cdot)\)	n/a	128	2
3150.2.l	\(\chi_{3150}(1201, \cdot)\)	n/a	304	2
3150.2.m	\(\chi_{3150}(1457, \cdot)\)	3150.2.m.a	4	2
		3150.2.m.b	4
		3150.2.m.c	4
		3150.2.m.d	4
		3150.2.m.e	4
		3150.2.m.f	4
		3150.2.m.g	8
		3150.2.m.h	8
		3150.2.m.i	8
		3150.2.m.j	8
		3150.2.m.k	8
		3150.2.m.l	8
3150.2.p	\(\chi_{3150}(307, \cdot)\)	n/a	120	2
3150.2.q	\(\chi_{3150}(631, \cdot)\)	n/a	296	4
3150.2.s	\(\chi_{3150}(299, \cdot)\)	n/a	288	2
3150.2.u	\(\chi_{3150}(551, \cdot)\)	n/a	304	2
3150.2.v	\(\chi_{3150}(1549, \cdot)\)	n/a	120	2
3150.2.ba	\(\chi_{3150}(799, \cdot)\)	n/a	216	2
3150.2.bb	\(\chi_{3150}(499, \cdot)\)	n/a	288	2
3150.2.bf	\(\chi_{3150}(1151, \cdot)\)	3150.2.bf.a	8	2
		3150.2.bf.b	8
		3150.2.bf.c	8
		3150.2.bf.d	24
		3150.2.bf.e	24
		3150.2.bf.f	32
3150.2.bg	\(\chi_{3150}(1049, \cdot)\)	n/a	288	2
3150.2.bj	\(\chi_{3150}(2399, \cdot)\)	n/a	288	2
3150.2.bl	\(\chi_{3150}(101, \cdot)\)	n/a	304	2
3150.2.bm	\(\chi_{3150}(1301, \cdot)\)	n/a	304	2
3150.2.bp	\(\chi_{3150}(899, \cdot)\)	3150.2.bp.a	8	2
		3150.2.bp.b	8
		3150.2.bp.c	8
		3150.2.bp.d	8
		3150.2.bp.e	8
		3150.2.bp.f	8
		3150.2.bp.g	24
		3150.2.bp.h	24
3150.2.br	\(\chi_{3150}(949, \cdot)\)	n/a	288	2
3150.2.bu	\(\chi_{3150}(379, \cdot)\)	n/a	304	4
3150.2.bx	\(\chi_{3150}(629, \cdot)\)	n/a	320	4
3150.2.bz	\(\chi_{3150}(881, \cdot)\)	n/a	320	4
3150.2.cb	\(\chi_{3150}(443, \cdot)\)	n/a	576	4
3150.2.cd	\(\chi_{3150}(1207, \cdot)\)	n/a	240	4
3150.2.ce	\(\chi_{3150}(493, \cdot)\)	n/a	576	4
3150.2.ch	\(\chi_{3150}(643, \cdot)\)	n/a	576	4
3150.2.ci	\(\chi_{3150}(407, \cdot)\)	n/a	432	4
3150.2.cl	\(\chi_{3150}(893, \cdot)\)	n/a	576	4
3150.2.cm	\(\chi_{3150}(107, \cdot)\)	n/a	192	4
3150.2.co	\(\chi_{3150}(157, \cdot)\)	n/a	576	4
3150.2.cq	\(\chi_{3150}(331, \cdot)\)	n/a	1920	8
3150.2.cr	\(\chi_{3150}(361, \cdot)\)	n/a	800	8
3150.2.cs	\(\chi_{3150}(211, \cdot)\)	n/a	1440	8
3150.2.ct	\(\chi_{3150}(121, \cdot)\)	n/a	1920	8
3150.2.cu	\(\chi_{3150}(433, \cdot)\)	n/a	800	8
3150.2.cx	\(\chi_{3150}(197, \cdot)\)	n/a	480	8
3150.2.cz	\(\chi_{3150}(79, \cdot)\)	n/a	1920	8
3150.2.db	\(\chi_{3150}(89, \cdot)\)	n/a	640	8
3150.2.de	\(\chi_{3150}(41, \cdot)\)	n/a	1920	8
3150.2.df	\(\chi_{3150}(131, \cdot)\)	n/a	1920	8
3150.2.dh	\(\chi_{3150}(479, \cdot)\)	n/a	1920	8
3150.2.dk	\(\chi_{3150}(209, \cdot)\)	n/a	1920	8
3150.2.dl	\(\chi_{3150}(341, \cdot)\)	n/a	640	8
3150.2.dp	\(\chi_{3150}(529, \cdot)\)	n/a	1920	8
3150.2.dq	\(\chi_{3150}(169, \cdot)\)	n/a	1440	8
3150.2.dv	\(\chi_{3150}(109, \cdot)\)	n/a	800	8
3150.2.dw	\(\chi_{3150}(311, \cdot)\)	n/a	1920	8
3150.2.dy	\(\chi_{3150}(59, \cdot)\)	n/a	1920	8
3150.2.eb	\(\chi_{3150}(187, \cdot)\)	n/a	3840	16
3150.2.ed	\(\chi_{3150}(53, \cdot)\)	n/a	1280	16
3150.2.ee	\(\chi_{3150}(23, \cdot)\)	n/a	3840	16
3150.2.eh	\(\chi_{3150}(113, \cdot)\)	n/a	2880	16
3150.2.ei	\(\chi_{3150}(13, \cdot)\)	n/a	3840	16
3150.2.el	\(\chi_{3150}(103, \cdot)\)	n/a	3840	16
3150.2.em	\(\chi_{3150}(73, \cdot)\)	n/a	1600	16
3150.2.eo	\(\chi_{3150}(317, \cdot)\)	n/a	3840	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3150))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3150)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1050))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1575))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3150))\)\(^{\oplus 1}\)