Space of modular forms of level 1275 and weight 4

• Label: 1275.4
• Level: 1275
• Weight: 4
• Dimension: 118004
• Nonzero newspaces: 36
• Sturm bound: 460800
• Trace bound: 14

Defining parameters

Level:	\( N \)	=	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(460800\)
Trace bound:			\(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1275))\).

	Total	New	Old
Modular forms	174592	119236	55356
Cusp forms	171008	118004	53004
Eisenstein series	3584	1232	2352

Trace form

118004 * q + 16 * q^2 - 108 * q^3 - 264 * q^4 + 12 * q^5 - 132 * q^6 - 248 * q^7 - 144 * q^8 - 156 * q^9 - 408 * q^10 + 444 * q^12 + 424 * q^13 + 736 * q^14 + 240 * q^15 - 952 * q^16 - 816 * q^17 - 1812 * q^18 - 1832 * q^19 - 312 * q^20 - 1908 * q^21 + 1080 * q^22 + 1024 * q^23 + 3496 * q^24 + 2836 * q^25 + 4752 * q^26 + 2724 * q^27 + 5208 * q^28 + 2952 * q^29 + 1644 * q^30 - 904 * q^31 - 6496 * q^32 - 3100 * q^33 - 8848 * q^34 - 4480 * q^35 - 4308 * q^36 - 8692 * q^37 - 12568 * q^38 - 8868 * q^39 - 8720 * q^40 - 2376 * q^41 + 484 * q^42 + 5496 * q^43 + 13160 * q^44 + 4784 * q^45 + 14120 * q^46 + 7808 * q^47 + 12912 * q^48 + 9212 * q^49 + 16448 * q^50 + 3232 * q^51 + 15360 * q^52 + 10540 * q^53 + 13320 * q^54 + 2776 * q^55 + 6880 * q^56 + 5508 * q^57 - 3808 * q^58 - 4256 * q^59 - 276 * q^60 - 4840 * q^61 - 24296 * q^62 - 6412 * q^63 - 27040 * q^64 - 2444 * q^65 - 6988 * q^66 - 3944 * q^67 - 43072 * q^68 - 29484 * q^69 - 35592 * q^70 - 28224 * q^71 - 45116 * q^72 - 43408 * q^73 - 29008 * q^74 - 19688 * q^75 - 6960 * q^76 + 7840 * q^77 + 6424 * q^78 + 22104 * q^79 + 42968 * q^80 + 6844 * q^81 + 68056 * q^82 + 16416 * q^83 + 47572 * q^84 + 19462 * q^85 + 34352 * q^86 + 16948 * q^87 + 89496 * q^88 + 14700 * q^89 + 23388 * q^90 + 42968 * q^91 + 52784 * q^92 + 31276 * q^93 + 52280 * q^94 + 25232 * q^95 + 21148 * q^96 + 29592 * q^97 + 6544 * q^98 + 848 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1275))\)

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
1275.4.a	\(\chi_{1275}(1, \cdot)\)	1275.4.a.a	1	1
		1275.4.a.b	1
		1275.4.a.c	1
		1275.4.a.d	1
		1275.4.a.e	1
		1275.4.a.f	1
		1275.4.a.g	1
		1275.4.a.h	1
		1275.4.a.i	1
		1275.4.a.j	1
		1275.4.a.k	1
		1275.4.a.l	2
		1275.4.a.m	2
		1275.4.a.n	2
		1275.4.a.o	2
		1275.4.a.p	2
		1275.4.a.q	3
		1275.4.a.r	5
		1275.4.a.s	5
		1275.4.a.t	5
		1275.4.a.u	5
		1275.4.a.v	6
		1275.4.a.w	6
		1275.4.a.x	7
		1275.4.a.y	7
		1275.4.a.z	8
		1275.4.a.ba	8
		1275.4.a.bb	9
		1275.4.a.bc	9
		1275.4.a.bd	10
		1275.4.a.be	10
		1275.4.a.bf	14
		1275.4.a.bg	14
1275.4.b	\(\chi_{1275}(1174, \cdot)\)	n/a	144	1
1275.4.d	\(\chi_{1275}(424, \cdot)\)	n/a	160	1
1275.4.g	\(\chi_{1275}(526, \cdot)\)	n/a	172	1
1275.4.j	\(\chi_{1275}(676, \cdot)\)	n/a	344	2
1275.4.k	\(\chi_{1275}(1007, \cdot)\)	n/a	640	2
1275.4.m	\(\chi_{1275}(443, \cdot)\)	n/a	576	2
1275.4.o	\(\chi_{1275}(407, \cdot)\)	n/a	640	2
1275.4.r	\(\chi_{1275}(293, \cdot)\)	n/a	640	2
1275.4.s	\(\chi_{1275}(574, \cdot)\)	n/a	320	2
1275.4.u	\(\chi_{1275}(256, \cdot)\)	n/a	960	4
1275.4.w	\(\chi_{1275}(332, \cdot)\)	n/a	1280	4
1275.4.x	\(\chi_{1275}(76, \cdot)\)	n/a	680	4
1275.4.ba	\(\chi_{1275}(49, \cdot)\)	n/a	656	4
1275.4.bb	\(\chi_{1275}(32, \cdot)\)	n/a	1280	4
1275.4.bd	\(\chi_{1275}(16, \cdot)\)	n/a	1072	4
1275.4.bh	\(\chi_{1275}(154, \cdot)\)	n/a	960	4
1275.4.bj	\(\chi_{1275}(169, \cdot)\)	n/a	1088	4
1275.4.bl	\(\chi_{1275}(7, \cdot)\)	n/a	1296	8
1275.4.bm	\(\chi_{1275}(74, \cdot)\)	n/a	2560	8
1275.4.bo	\(\chi_{1275}(176, \cdot)\)	n/a	2688	8
1275.4.bq	\(\chi_{1275}(82, \cdot)\)	n/a	1296	8
1275.4.bt	\(\chi_{1275}(4, \cdot)\)	n/a	2176	8
1275.4.bv	\(\chi_{1275}(98, \cdot)\)	n/a	4288	8
1275.4.bw	\(\chi_{1275}(152, \cdot)\)	n/a	4288	8
1275.4.by	\(\chi_{1275}(137, \cdot)\)	n/a	3840	8
1275.4.ca	\(\chi_{1275}(38, \cdot)\)	n/a	4288	8
1275.4.cc	\(\chi_{1275}(106, \cdot)\)	n/a	2144	8
1275.4.ce	\(\chi_{1275}(2, \cdot)\)	n/a	8576	16
1275.4.cg	\(\chi_{1275}(19, \cdot)\)	n/a	4288	16
1275.4.cj	\(\chi_{1275}(121, \cdot)\)	n/a	4352	16
1275.4.cl	\(\chi_{1275}(53, \cdot)\)	n/a	8576	16
1275.4.cn	\(\chi_{1275}(22, \cdot)\)	n/a	8640	32
1275.4.cp	\(\chi_{1275}(11, \cdot)\)	n/a	17152	32
1275.4.cr	\(\chi_{1275}(14, \cdot)\)	n/a	17152	32
1275.4.cs	\(\chi_{1275}(73, \cdot)\)	n/a	8640	32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1275))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1275)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1275))\)\(^{\oplus 1}\)