Space of modular forms of level 1260 and weight 4

• Label: 1260.4
• Level: 1260
• Weight: 4
• Dimension: 50202
• Nonzero newspaces: 60
• Sturm bound: 331776
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(331776\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1260))\).

	Total	New	Old
Modular forms	126336	50738	75598
Cusp forms	122496	50202	72294
Eisenstein series	3840	536	3304

Trace form

50202 * q - 18 * q^2 - 12 * q^3 + 34 * q^4 - 44 * q^5 + 44 * q^6 - 28 * q^7 - 42 * q^8 + 36 * q^9 - 196 * q^10 + 332 * q^11 - 32 * q^12 + 396 * q^13 + 150 * q^14 - 144 * q^15 + 814 * q^16 + 80 * q^17 - 424 * q^18 + 148 * q^19 - 86 * q^20 + 236 * q^21 - 1144 * q^22 + 1200 * q^23 + 60 * q^24 - 2742 * q^25 - 1900 * q^26 + 696 * q^27 - 1486 * q^28 - 12 * q^29 - 714 * q^30 + 1392 * q^31 + 4522 * q^32 - 1932 * q^33 + 960 * q^34 + 670 * q^35 + 3492 * q^36 - 928 * q^37 + 1316 * q^38 - 1832 * q^39 - 1142 * q^40 - 3080 * q^41 - 3208 * q^42 + 100 * q^43 - 5100 * q^44 - 576 * q^45 - 1788 * q^46 - 864 * q^47 - 9244 * q^48 - 9326 * q^49 - 1142 * q^50 + 2268 * q^51 - 1320 * q^52 - 2656 * q^53 - 2272 * q^54 - 2312 * q^55 + 3734 * q^56 - 3820 * q^57 + 6308 * q^58 - 4600 * q^59 + 4678 * q^60 + 48 * q^61 + 6536 * q^62 - 8912 * q^63 + 3310 * q^64 - 2336 * q^65 + 12052 * q^66 + 5692 * q^67 + 5488 * q^68 + 12712 * q^69 - 11202 * q^70 + 17808 * q^71 - 528 * q^72 + 9472 * q^73 - 6864 * q^74 + 2352 * q^75 + 888 * q^76 + 6180 * q^77 + 8072 * q^78 + 1600 * q^79 + 7250 * q^80 - 8340 * q^81 + 15740 * q^82 - 5796 * q^83 + 14924 * q^84 - 15772 * q^85 + 11324 * q^86 + 1768 * q^87 - 1384 * q^88 - 15596 * q^89 + 9306 * q^90 - 5276 * q^91 - 9236 * q^92 + 7744 * q^93 - 18040 * q^94 + 2220 * q^95 - 14368 * q^96 + 10956 * q^97 - 13686 * q^98 - 2408 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1260))\)

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
1260.4.a	\(\chi_{1260}(1, \cdot)\)	1260.4.a.a	1	1
		1260.4.a.b	1
		1260.4.a.c	1
		1260.4.a.d	1
		1260.4.a.e	1
		1260.4.a.f	1
		1260.4.a.g	1
		1260.4.a.h	1
		1260.4.a.i	1
		1260.4.a.j	1
		1260.4.a.k	1
		1260.4.a.l	1
		1260.4.a.m	2
		1260.4.a.n	2
		1260.4.a.o	2
		1260.4.a.p	3
		1260.4.a.q	3
		1260.4.a.r	3
		1260.4.a.s	3
1260.4.c	\(\chi_{1260}(811, \cdot)\)	n/a	240	1
1260.4.d	\(\chi_{1260}(881, \cdot)\)	1260.4.d.a	16	1
		1260.4.d.b	16
1260.4.f	\(\chi_{1260}(629, \cdot)\)	1260.4.f.a	48	1
1260.4.i	\(\chi_{1260}(559, \cdot)\)	n/a	356	1
1260.4.k	\(\chi_{1260}(1009, \cdot)\)	1260.4.k.a	2	1
		1260.4.k.b	2
		1260.4.k.c	2
		1260.4.k.d	4
		1260.4.k.e	6
		1260.4.k.f	12
		1260.4.k.g	16
1260.4.l	\(\chi_{1260}(1079, \cdot)\)	n/a	216	1
1260.4.n	\(\chi_{1260}(71, \cdot)\)	n/a	144	1
1260.4.q	\(\chi_{1260}(121, \cdot)\)	n/a	192	2
1260.4.r	\(\chi_{1260}(421, \cdot)\)	n/a	144	2
1260.4.s	\(\chi_{1260}(361, \cdot)\)	1260.4.s.a	2	2
		1260.4.s.b	2
		1260.4.s.c	2
		1260.4.s.d	4
		1260.4.s.e	4
		1260.4.s.f	4
		1260.4.s.g	6
		1260.4.s.h	8
		1260.4.s.i	8
		1260.4.s.j	8
		1260.4.s.k	16
		1260.4.s.l	16
1260.4.t	\(\chi_{1260}(961, \cdot)\)	n/a	192	2
1260.4.v	\(\chi_{1260}(197, \cdot)\)	1260.4.v.a	36	2
		1260.4.v.b	36
1260.4.w	\(\chi_{1260}(127, \cdot)\)	n/a	540	2
1260.4.z	\(\chi_{1260}(503, \cdot)\)	n/a	576	2
1260.4.ba	\(\chi_{1260}(433, \cdot)\)	n/a	120	2
1260.4.bc	\(\chi_{1260}(439, \cdot)\)	n/a	1712	2
1260.4.bf	\(\chi_{1260}(689, \cdot)\)	n/a	288	2
1260.4.bh	\(\chi_{1260}(941, \cdot)\)	n/a	192	2
1260.4.bi	\(\chi_{1260}(31, \cdot)\)	n/a	1152	2
1260.4.bl	\(\chi_{1260}(179, \cdot)\)	n/a	576	2
1260.4.bm	\(\chi_{1260}(109, \cdot)\)	n/a	120	2
1260.4.bo	\(\chi_{1260}(491, \cdot)\)	n/a	864	2
1260.4.bs	\(\chi_{1260}(11, \cdot)\)	n/a	1152	2
1260.4.bv	\(\chi_{1260}(169, \cdot)\)	n/a	216	2
1260.4.bx	\(\chi_{1260}(779, \cdot)\)	n/a	1712	2
1260.4.by	\(\chi_{1260}(529, \cdot)\)	n/a	288	2
1260.4.ca	\(\chi_{1260}(239, \cdot)\)	n/a	1296	2
1260.4.ce	\(\chi_{1260}(431, \cdot)\)	n/a	384	2
1260.4.cg	\(\chi_{1260}(341, \cdot)\)	1260.4.cg.a	32	2
		1260.4.cg.b	32
1260.4.ch	\(\chi_{1260}(271, \cdot)\)	n/a	480	2
1260.4.cj	\(\chi_{1260}(209, \cdot)\)	n/a	288	2
1260.4.cl	\(\chi_{1260}(619, \cdot)\)	n/a	1712	2
1260.4.co	\(\chi_{1260}(509, \cdot)\)	n/a	288	2
1260.4.cq	\(\chi_{1260}(139, \cdot)\)	n/a	1712	2
1260.4.cs	\(\chi_{1260}(391, \cdot)\)	n/a	1152	2
1260.4.cu	\(\chi_{1260}(101, \cdot)\)	n/a	192	2
1260.4.cv	\(\chi_{1260}(871, \cdot)\)	n/a	1152	2
1260.4.cx	\(\chi_{1260}(41, \cdot)\)	n/a	192	2
1260.4.cz	\(\chi_{1260}(19, \cdot)\)	n/a	712	2
1260.4.dc	\(\chi_{1260}(89, \cdot)\)	1260.4.dc.a	96	2
1260.4.df	\(\chi_{1260}(191, \cdot)\)	n/a	1152	2
1260.4.dh	\(\chi_{1260}(599, \cdot)\)	n/a	1712	2
1260.4.di	\(\chi_{1260}(709, \cdot)\)	n/a	288	2
1260.4.dl	\(\chi_{1260}(67, \cdot)\)	n/a	3424	4
1260.4.dm	\(\chi_{1260}(317, \cdot)\)	n/a	576	4
1260.4.do	\(\chi_{1260}(83, \cdot)\)	n/a	3424	4
1260.4.dq	\(\chi_{1260}(73, \cdot)\)	n/a	240	4
1260.4.ds	\(\chi_{1260}(493, \cdot)\)	n/a	576	4
1260.4.dv	\(\chi_{1260}(227, \cdot)\)	n/a	3424	4
1260.4.dx	\(\chi_{1260}(143, \cdot)\)	n/a	1152	4
1260.4.dz	\(\chi_{1260}(13, \cdot)\)	n/a	576	4
1260.4.ea	\(\chi_{1260}(113, \cdot)\)	n/a	432	4
1260.4.ec	\(\chi_{1260}(163, \cdot)\)	n/a	1424	4
1260.4.ee	\(\chi_{1260}(247, \cdot)\)	n/a	3424	4
1260.4.eh	\(\chi_{1260}(137, \cdot)\)	n/a	576	4
1260.4.ej	\(\chi_{1260}(53, \cdot)\)	n/a	192	4
1260.4.el	\(\chi_{1260}(43, \cdot)\)	n/a	2592	4
1260.4.en	\(\chi_{1260}(157, \cdot)\)	n/a	576	4
1260.4.eo	\(\chi_{1260}(47, \cdot)\)	n/a	3424	4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1260))\) into lower level spaces

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