Space of modular forms of level 1260 and weight 2

• Label: 1260.2
• Level: 1260
• Weight: 2
• Dimension: 16558
• Nonzero newspaces: 60
• Sturm bound: 165888
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(165888\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1260))\).

	Total	New	Old
Modular forms	43392	17094	26298
Cusp forms	39553	16558	22995
Eisenstein series	3839	536	3303

Trace form

16558 * q - 18 * q^2 - 30 * q^4 - 43 * q^5 - 52 * q^6 - 42 * q^8 - 72 * q^9 - 78 * q^10 - 50 * q^11 + 16 * q^12 - 108 * q^13 - 6 * q^14 - 18 * q^15 - 18 * q^16 - 86 * q^17 + 80 * q^18 - 82 * q^19 + 98 * q^20 - 154 * q^21 + 72 * q^22 - 18 * q^23 + 60 * q^24 - 59 * q^25 + 148 * q^26 + 12 * q^27 + 50 * q^28 - 24 * q^29 + 54 * q^30 + 38 * q^31 + 122 * q^32 + 156 * q^33 + 216 * q^34 + 77 * q^35 - 60 * q^36 - 10 * q^37 + 160 * q^38 + 172 * q^39 + 162 * q^40 + 272 * q^41 + 92 * q^42 + 112 * q^43 + 204 * q^44 + 198 * q^45 + 128 * q^46 + 234 * q^47 + 164 * q^48 + 120 * q^49 - 10 * q^50 + 240 * q^51 + 152 * q^52 + 358 * q^53 + 80 * q^54 + 94 * q^55 + 70 * q^56 + 200 * q^57 + 44 * q^58 + 202 * q^59 - 122 * q^60 + 86 * q^61 - 128 * q^62 + 166 * q^63 - 114 * q^64 + 242 * q^65 - 284 * q^66 - 34 * q^67 - 280 * q^68 + 76 * q^69 + 6 * q^70 + 24 * q^71 - 432 * q^72 + 90 * q^73 - 468 * q^74 - 42 * q^75 - 152 * q^76 + 276 * q^77 - 520 * q^78 + 102 * q^79 - 350 * q^80 - 72 * q^81 - 52 * q^82 - 24 * q^83 - 340 * q^84 + 150 * q^85 - 404 * q^86 - 152 * q^87 - 168 * q^88 + 266 * q^89 - 426 * q^90 + 128 * q^91 - 484 * q^92 + 184 * q^93 - 156 * q^94 + 69 * q^95 - 448 * q^96 + 436 * q^97 - 342 * q^98 - 44 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1260))\)

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
1260.2.a	\(\chi_{1260}(1, \cdot)\)	1260.2.a.a	1	1
		1260.2.a.b	1
		1260.2.a.c	1
		1260.2.a.d	1
		1260.2.a.e	1
		1260.2.a.f	1
		1260.2.a.g	1
		1260.2.a.h	1
		1260.2.a.i	1
		1260.2.a.j	1
1260.2.c	\(\chi_{1260}(811, \cdot)\)	1260.2.c.a	4	1
		1260.2.c.b	4
		1260.2.c.c	8
		1260.2.c.d	16
		1260.2.c.e	16
		1260.2.c.f	32
1260.2.d	\(\chi_{1260}(881, \cdot)\)	1260.2.d.a	4	1
		1260.2.d.b	4
1260.2.f	\(\chi_{1260}(629, \cdot)\)	1260.2.f.a	8	1
		1260.2.f.b	8
1260.2.i	\(\chi_{1260}(559, \cdot)\)	n/a	116	1
1260.2.k	\(\chi_{1260}(1009, \cdot)\)	1260.2.k.a	2	1
		1260.2.k.b	2
		1260.2.k.c	2
		1260.2.k.d	2
		1260.2.k.e	8
1260.2.l	\(\chi_{1260}(1079, \cdot)\)	1260.2.l.a	4	1
		1260.2.l.b	4
		1260.2.l.c	32
		1260.2.l.d	32
1260.2.n	\(\chi_{1260}(71, \cdot)\)	1260.2.n.a	24	1
		1260.2.n.b	24
1260.2.q	\(\chi_{1260}(121, \cdot)\)	1260.2.q.a	2	2
		1260.2.q.b	2
		1260.2.q.c	2
		1260.2.q.d	26
		1260.2.q.e	32
1260.2.r	\(\chi_{1260}(421, \cdot)\)	1260.2.r.a	2	2
		1260.2.r.b	2
		1260.2.r.c	2
		1260.2.r.d	2
		1260.2.r.e	2
		1260.2.r.f	8
		1260.2.r.g	8
		1260.2.r.h	8
		1260.2.r.i	14
1260.2.s	\(\chi_{1260}(361, \cdot)\)	1260.2.s.a	2	2
		1260.2.s.b	2
		1260.2.s.c	2
		1260.2.s.d	2
		1260.2.s.e	4
		1260.2.s.f	4
		1260.2.s.g	6
		1260.2.s.h	6
1260.2.t	\(\chi_{1260}(961, \cdot)\)	1260.2.t.a	2	2
		1260.2.t.b	2
		1260.2.t.c	2
		1260.2.t.d	26
		1260.2.t.e	32
1260.2.v	\(\chi_{1260}(197, \cdot)\)	1260.2.v.a	12	2
		1260.2.v.b	12
1260.2.w	\(\chi_{1260}(127, \cdot)\)	n/a	180	2
1260.2.z	\(\chi_{1260}(503, \cdot)\)	n/a	192	2
1260.2.ba	\(\chi_{1260}(433, \cdot)\)	1260.2.ba.a	8	2
		1260.2.ba.b	16
		1260.2.ba.c	16
1260.2.bc	\(\chi_{1260}(439, \cdot)\)	n/a	560	2
1260.2.bf	\(\chi_{1260}(689, \cdot)\)	1260.2.bf.a	96	2
1260.2.bh	\(\chi_{1260}(941, \cdot)\)	1260.2.bh.a	2	2
		1260.2.bh.b	2
		1260.2.bh.c	2
		1260.2.bh.d	28
		1260.2.bh.e	30
1260.2.bi	\(\chi_{1260}(31, \cdot)\)	n/a	384	2
1260.2.bl	\(\chi_{1260}(179, \cdot)\)	n/a	192	2
1260.2.bm	\(\chi_{1260}(109, \cdot)\)	1260.2.bm.a	4	2
		1260.2.bm.b	4
		1260.2.bm.c	16
		1260.2.bm.d	16
1260.2.bo	\(\chi_{1260}(491, \cdot)\)	n/a	288	2
1260.2.bs	\(\chi_{1260}(11, \cdot)\)	n/a	384	2
1260.2.bv	\(\chi_{1260}(169, \cdot)\)	1260.2.bv.a	4	2
		1260.2.bv.b	68
1260.2.bx	\(\chi_{1260}(779, \cdot)\)	n/a	560	2
1260.2.by	\(\chi_{1260}(529, \cdot)\)	1260.2.by.a	4	2
		1260.2.by.b	92
1260.2.ca	\(\chi_{1260}(239, \cdot)\)	n/a	432	2
1260.2.ce	\(\chi_{1260}(431, \cdot)\)	n/a	128	2
1260.2.cg	\(\chi_{1260}(341, \cdot)\)	1260.2.cg.a	12	2
		1260.2.cg.b	12
1260.2.ch	\(\chi_{1260}(271, \cdot)\)	n/a	160	2
1260.2.cj	\(\chi_{1260}(209, \cdot)\)	1260.2.cj.a	8	2
		1260.2.cj.b	8
		1260.2.cj.c	80
1260.2.cl	\(\chi_{1260}(619, \cdot)\)	n/a	560	2
1260.2.co	\(\chi_{1260}(509, \cdot)\)	1260.2.co.a	96	2
1260.2.cq	\(\chi_{1260}(139, \cdot)\)	n/a	560	2
1260.2.cs	\(\chi_{1260}(391, \cdot)\)	n/a	384	2
1260.2.cu	\(\chi_{1260}(101, \cdot)\)	1260.2.cu.a	2	2
		1260.2.cu.b	2
		1260.2.cu.c	2
		1260.2.cu.d	28
		1260.2.cu.e	30
1260.2.cv	\(\chi_{1260}(871, \cdot)\)	n/a	384	2
1260.2.cx	\(\chi_{1260}(41, \cdot)\)	1260.2.cx.a	2	2
		1260.2.cx.b	2
		1260.2.cx.c	30
		1260.2.cx.d	30
1260.2.cz	\(\chi_{1260}(19, \cdot)\)	n/a	232	2
1260.2.dc	\(\chi_{1260}(89, \cdot)\)	1260.2.dc.a	32	2
1260.2.df	\(\chi_{1260}(191, \cdot)\)	n/a	384	2
1260.2.dh	\(\chi_{1260}(599, \cdot)\)	n/a	560	2
1260.2.di	\(\chi_{1260}(709, \cdot)\)	1260.2.di.a	4	2
		1260.2.di.b	92
1260.2.dl	\(\chi_{1260}(67, \cdot)\)	n/a	1120	4
1260.2.dm	\(\chi_{1260}(317, \cdot)\)	n/a	192	4
1260.2.do	\(\chi_{1260}(83, \cdot)\)	n/a	1120	4
1260.2.dq	\(\chi_{1260}(73, \cdot)\)	1260.2.dq.a	16	4
		1260.2.dq.b	32
		1260.2.dq.c	32
1260.2.ds	\(\chi_{1260}(493, \cdot)\)	n/a	192	4
1260.2.dv	\(\chi_{1260}(227, \cdot)\)	n/a	1120	4
1260.2.dx	\(\chi_{1260}(143, \cdot)\)	n/a	384	4
1260.2.dz	\(\chi_{1260}(13, \cdot)\)	n/a	192	4
1260.2.ea	\(\chi_{1260}(113, \cdot)\)	n/a	144	4
1260.2.ec	\(\chi_{1260}(163, \cdot)\)	n/a	464	4
1260.2.ee	\(\chi_{1260}(247, \cdot)\)	n/a	1120	4
1260.2.eh	\(\chi_{1260}(137, \cdot)\)	n/a	192	4
1260.2.ej	\(\chi_{1260}(53, \cdot)\)	1260.2.ej.a	64	4
1260.2.el	\(\chi_{1260}(43, \cdot)\)	n/a	864	4
1260.2.en	\(\chi_{1260}(157, \cdot)\)	n/a	192	4
1260.2.eo	\(\chi_{1260}(47, \cdot)\)	n/a	1120	4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1260))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1260)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1260))\)\(^{\oplus 1}\)