Space of modular forms of level 2499 and weight 4

• Label: 2499.4
• Level: 2499
• Weight: 4
• Dimension: 482672
• Nonzero newspaces: 40
• Sturm bound: 1806336
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 2499 = 3 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(1806336\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2499))\).

	Total	New	Old
Modular forms	681216	485584	195632
Cusp forms	673536	482672	190864
Eisenstein series	7680	2912	4768

Trace form

482672 * q - 194 * q^3 - 436 * q^4 - 96 * q^5 - 350 * q^6 - 600 * q^7 + 216 * q^8 - 50 * q^9 - 12 * q^10 + 224 * q^11 - 494 * q^12 - 812 * q^13 - 624 * q^14 - 1490 * q^15 - 1796 * q^16 - 280 * q^17 + 178 * q^18 + 1660 * q^19 + 3952 * q^20 + 924 * q^21 + 1452 * q^22 - 256 * q^23 + 2242 * q^24 + 340 * q^25 + 888 * q^26 - 638 * q^27 - 2712 * q^28 - 3112 * q^29 - 7670 * q^30 - 5140 * q^31 - 7352 * q^32 - 4458 * q^33 - 5230 * q^34 + 168 * q^35 + 302 * q^36 - 5476 * q^37 - 4616 * q^38 - 882 * q^39 - 5692 * q^40 + 344 * q^41 + 5406 * q^42 + 9644 * q^43 + 27776 * q^44 + 12854 * q^45 + 27524 * q^46 + 10896 * q^47 + 14048 * q^48 + 10944 * q^49 + 2424 * q^50 - 1237 * q^51 + 2548 * q^52 - 264 * q^53 - 10110 * q^54 + 3724 * q^55 - 2652 * q^56 - 250 * q^57 + 2164 * q^58 - 11440 * q^59 - 12838 * q^60 - 11428 * q^61 - 19408 * q^62 + 2052 * q^63 - 6300 * q^64 - 5304 * q^65 - 5022 * q^66 - 1012 * q^67 - 10352 * q^68 - 10822 * q^69 - 7500 * q^70 - 2352 * q^71 - 20078 * q^72 - 18316 * q^73 - 11448 * q^74 - 10286 * q^75 - 23564 * q^76 - 360 * q^77 - 4338 * q^78 - 1748 * q^79 - 40556 * q^80 - 7218 * q^81 - 29688 * q^82 - 14032 * q^83 - 23604 * q^84 - 3706 * q^85 - 5164 * q^86 - 6926 * q^87 - 15016 * q^88 - 1680 * q^89 + 25040 * q^90 + 19596 * q^91 + 16100 * q^92 + 37542 * q^93 + 66632 * q^94 + 68192 * q^95 + 52016 * q^96 + 37904 * q^97 + 102108 * q^98 - 23776 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2499))\)

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
2499.4.a	\(\chi_{2499}(1, \cdot)\)	2499.4.a.a	1	1
		2499.4.a.b	1
		2499.4.a.c	1
		2499.4.a.d	1
		2499.4.a.e	1
		2499.4.a.f	1
		2499.4.a.g	1
		2499.4.a.h	1
		2499.4.a.i	1
		2499.4.a.j	1
		2499.4.a.k	1
		2499.4.a.l	2
		2499.4.a.m	3
		2499.4.a.n	3
		2499.4.a.o	4
		2499.4.a.p	6
		2499.4.a.q	6
		2499.4.a.r	6
		2499.4.a.s	7
		2499.4.a.t	7
		2499.4.a.u	7
		2499.4.a.v	8
		2499.4.a.w	8
		2499.4.a.x	14
		2499.4.a.y	14
		2499.4.a.z	15
		2499.4.a.ba	15
		2499.4.a.bb	15
		2499.4.a.bc	15
		2499.4.a.bd	16
		2499.4.a.be	16
		2499.4.a.bf	17
		2499.4.a.bg	17
		2499.4.a.bh	20
		2499.4.a.bi	20
		2499.4.a.bj	28
		2499.4.a.bk	28
2499.4.c	\(\chi_{2499}(2498, \cdot)\)	n/a	712	1
2499.4.d	\(\chi_{2499}(1616, \cdot)\)	n/a	640	1
2499.4.f	\(\chi_{2499}(883, \cdot)\)	n/a	368	1
2499.4.i	\(\chi_{2499}(1684, \cdot)\)	n/a	640	2
2499.4.k	\(\chi_{2499}(1177, \cdot)\)	n/a	736	2
2499.4.l	\(\chi_{2499}(293, \cdot)\)	n/a	1424	2
2499.4.p	\(\chi_{2499}(67, \cdot)\)	n/a	720	2
2499.4.r	\(\chi_{2499}(2126, \cdot)\)	n/a	1280	2
2499.4.s	\(\chi_{2499}(509, \cdot)\)	n/a	1424	2
2499.4.u	\(\chi_{2499}(358, \cdot)\)	n/a	2688	6
2499.4.v	\(\chi_{2499}(1324, \cdot)\)	n/a	1480	4
2499.4.x	\(\chi_{2499}(440, \cdot)\)	n/a	2848	4
2499.4.z	\(\chi_{2499}(803, \cdot)\)	n/a	2848	4
2499.4.bc	\(\chi_{2499}(361, \cdot)\)	n/a	1440	4
2499.4.bf	\(\chi_{2499}(169, \cdot)\)	n/a	3024	6
2499.4.bh	\(\chi_{2499}(188, \cdot)\)	n/a	5376	6
2499.4.bi	\(\chi_{2499}(356, \cdot)\)	n/a	6024	6
2499.4.bk	\(\chi_{2499}(97, \cdot)\)	n/a	2880	8
2499.4.bn	\(\chi_{2499}(197, \cdot)\)	n/a	5824	8
2499.4.bo	\(\chi_{2499}(205, \cdot)\)	n/a	5376	12
2499.4.bq	\(\chi_{2499}(508, \cdot)\)	n/a	2880	8
2499.4.bs	\(\chi_{2499}(950, \cdot)\)	n/a	5696	8
2499.4.bu	\(\chi_{2499}(251, \cdot)\)	n/a	12048	12
2499.4.bv	\(\chi_{2499}(64, \cdot)\)	n/a	6048	12
2499.4.by	\(\chi_{2499}(101, \cdot)\)	n/a	12048	12
2499.4.bz	\(\chi_{2499}(290, \cdot)\)	n/a	10752	12
2499.4.cb	\(\chi_{2499}(16, \cdot)\)	n/a	6048	12
2499.4.cf	\(\chi_{2499}(31, \cdot)\)	n/a	5760	16
2499.4.cg	\(\chi_{2499}(116, \cdot)\)	n/a	11392	16
2499.4.cj	\(\chi_{2499}(83, \cdot)\)	n/a	24096	24
2499.4.cl	\(\chi_{2499}(43, \cdot)\)	n/a	12096	24
2499.4.cm	\(\chi_{2499}(4, \cdot)\)	n/a	12096	24
2499.4.cp	\(\chi_{2499}(38, \cdot)\)	n/a	24096	24
2499.4.cr	\(\chi_{2499}(139, \cdot)\)	n/a	24192	48
2499.4.cs	\(\chi_{2499}(29, \cdot)\)	n/a	48192	48
2499.4.cu	\(\chi_{2499}(26, \cdot)\)	n/a	48192	48
2499.4.cw	\(\chi_{2499}(25, \cdot)\)	n/a	24192	48
2499.4.cy	\(\chi_{2499}(10, \cdot)\)	n/a	48384	96
2499.4.db	\(\chi_{2499}(11, \cdot)\)	n/a	96384	96

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2499))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2499)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(833))\)\(^{\oplus 2}\)