Space of modular forms of level 2535 and weight 2

• Label: 2535.2
• Level: 2535
• Weight: 2
• Dimension: 153084
• Nonzero newspaces: 40
• Sturm bound: 908544
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(908544\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2535))\).

	Total	New	Old
Modular forms	230784	155540	75244
Cusp forms	223489	153084	70405
Eisenstein series	7295	2456	4839

Trace form

153084 * q - 4 * q^2 - 134 * q^3 - 272 * q^4 - 398 * q^6 - 256 * q^7 + 60 * q^8 - 124 * q^9 - 340 * q^10 + 32 * q^11 - 34 * q^12 - 240 * q^13 + 72 * q^14 - 176 * q^15 - 664 * q^16 + 56 * q^17 - 40 * q^18 - 120 * q^19 + 124 * q^20 - 300 * q^21 - 56 * q^22 + 72 * q^23 - 6 * q^24 - 372 * q^25 + 120 * q^26 - 110 * q^27 + 16 * q^28 + 88 * q^29 - 152 * q^30 - 728 * q^31 + 172 * q^32 - 116 * q^33 - 128 * q^34 + 40 * q^35 - 524 * q^36 - 288 * q^37 - 64 * q^38 - 176 * q^39 - 672 * q^40 + 136 * q^41 - 84 * q^42 - 48 * q^43 + 160 * q^44 - 222 * q^45 - 384 * q^46 + 152 * q^47 - 210 * q^48 + 24 * q^49 + 176 * q^50 - 296 * q^51 - 156 * q^52 + 128 * q^53 - 230 * q^54 - 436 * q^55 + 24 * q^56 - 100 * q^57 - 184 * q^58 - 16 * q^59 - 576 * q^60 - 592 * q^61 - 144 * q^62 - 372 * q^63 - 504 * q^64 - 102 * q^65 - 1132 * q^66 - 448 * q^67 - 488 * q^68 - 468 * q^69 - 732 * q^70 - 176 * q^71 - 744 * q^72 - 456 * q^73 - 224 * q^74 - 456 * q^75 - 1064 * q^76 - 96 * q^77 - 396 * q^78 - 488 * q^79 - 92 * q^80 - 628 * q^81 - 40 * q^82 + 72 * q^83 - 276 * q^84 - 232 * q^85 + 248 * q^86 - 64 * q^87 + 360 * q^88 + 384 * q^89 - 142 * q^90 - 568 * q^91 + 504 * q^92 + 84 * q^93 + 448 * q^94 + 320 * q^95 + 2 * q^96 + 168 * q^97 + 460 * q^98 + 164 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2535))\)

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
2535.2.a	\(\chi_{2535}(1, \cdot)\)	2535.2.a.a	1	1
		2535.2.a.b	1
		2535.2.a.c	1
		2535.2.a.d	1
		2535.2.a.e	1
		2535.2.a.f	1
		2535.2.a.g	1
		2535.2.a.h	1
		2535.2.a.i	1
		2535.2.a.j	1
		2535.2.a.k	1
		2535.2.a.l	1
		2535.2.a.m	1
		2535.2.a.n	2
		2535.2.a.o	2
		2535.2.a.p	2
		2535.2.a.q	2
		2535.2.a.r	2
		2535.2.a.s	2
		2535.2.a.t	3
		2535.2.a.u	3
		2535.2.a.v	3
		2535.2.a.w	3
		2535.2.a.x	3
		2535.2.a.y	3
		2535.2.a.z	3
		2535.2.a.ba	3
		2535.2.a.bb	3
		2535.2.a.bc	3
		2535.2.a.bd	3
		2535.2.a.be	3
		2535.2.a.bf	3
		2535.2.a.bg	3
		2535.2.a.bh	3
		2535.2.a.bi	4
		2535.2.a.bj	4
		2535.2.a.bk	4
		2535.2.a.bl	4
		2535.2.a.bm	9
		2535.2.a.bn	9
2535.2.b	\(\chi_{2535}(1351, \cdot)\)	n/a	104	1
2535.2.c	\(\chi_{2535}(2029, \cdot)\)	n/a	156	1
2535.2.h	\(\chi_{2535}(844, \cdot)\)	n/a	152	1
2535.2.i	\(\chi_{2535}(991, \cdot)\)	n/a	204	2
2535.2.k	\(\chi_{2535}(1282, \cdot)\)	n/a	308	2
2535.2.m	\(\chi_{2535}(677, \cdot)\)	n/a	576	2
2535.2.n	\(\chi_{2535}(239, \cdot)\)	n/a	576	2
2535.2.o	\(\chi_{2535}(746, \cdot)\)	n/a	408	2
2535.2.s	\(\chi_{2535}(1013, \cdot)\)	n/a	576	2
2535.2.t	\(\chi_{2535}(268, \cdot)\)	n/a	308	2
2535.2.v	\(\chi_{2535}(2344, \cdot)\)	n/a	304	2
2535.2.ba	\(\chi_{2535}(484, \cdot)\)	n/a	312	2
2535.2.bb	\(\chi_{2535}(316, \cdot)\)	n/a	204	2
2535.2.bd	\(\chi_{2535}(1333, \cdot)\)	n/a	616	4
2535.2.bf	\(\chi_{2535}(23, \cdot)\)	n/a	1152	4
2535.2.bg	\(\chi_{2535}(596, \cdot)\)	n/a	824	4
2535.2.bh	\(\chi_{2535}(89, \cdot)\)	n/a	1152	4
2535.2.bl	\(\chi_{2535}(653, \cdot)\)	n/a	1152	4
2535.2.bm	\(\chi_{2535}(418, \cdot)\)	n/a	616	4
2535.2.bo	\(\chi_{2535}(196, \cdot)\)	n/a	1440	12
2535.2.bp	\(\chi_{2535}(64, \cdot)\)	n/a	2208	12
2535.2.bu	\(\chi_{2535}(79, \cdot)\)	n/a	2160	12
2535.2.bv	\(\chi_{2535}(181, \cdot)\)	n/a	1440	12
2535.2.bw	\(\chi_{2535}(16, \cdot)\)	n/a	2928	24
2535.2.by	\(\chi_{2535}(73, \cdot)\)	n/a	4368	24
2535.2.bz	\(\chi_{2535}(38, \cdot)\)	n/a	8640	24
2535.2.cd	\(\chi_{2535}(86, \cdot)\)	n/a	5856	24
2535.2.ce	\(\chi_{2535}(44, \cdot)\)	n/a	8640	24
2535.2.cf	\(\chi_{2535}(53, \cdot)\)	n/a	8640	24
2535.2.ch	\(\chi_{2535}(112, \cdot)\)	n/a	4368	24
2535.2.cj	\(\chi_{2535}(121, \cdot)\)	n/a	2928	24
2535.2.ck	\(\chi_{2535}(94, \cdot)\)	n/a	4320	24
2535.2.cp	\(\chi_{2535}(4, \cdot)\)	n/a	4416	24
2535.2.cr	\(\chi_{2535}(7, \cdot)\)	n/a	8736	48
2535.2.cs	\(\chi_{2535}(68, \cdot)\)	n/a	17280	48
2535.2.cw	\(\chi_{2535}(59, \cdot)\)	n/a	17280	48
2535.2.cx	\(\chi_{2535}(11, \cdot)\)	n/a	11616	48
2535.2.cy	\(\chi_{2535}(17, \cdot)\)	n/a	17280	48
2535.2.da	\(\chi_{2535}(67, \cdot)\)	n/a	8736	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2535))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2535)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2535))\)\(^{\oplus 1}\)