Space of modular forms of level 2299 and weight 2

• Label: 2299.2
• Level: 2299
• Weight: 2
• Dimension: 210638
• Nonzero newspaces: 24
• Sturm bound: 871200
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 2299 = 11^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(871200\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2299))\).

	Total	New	Old
Modular forms	220680	215414	5266
Cusp forms	214921	210638	4283
Eisenstein series	5759	4776	983

Trace form

210638 * q - 723 * q^2 - 721 * q^3 - 715 * q^4 - 717 * q^5 - 725 * q^6 - 733 * q^7 - 739 * q^8 - 743 * q^9 - 753 * q^10 - 810 * q^11 - 1405 * q^12 - 733 * q^13 - 759 * q^14 - 779 * q^15 - 823 * q^16 - 762 * q^17 - 807 * q^18 - 805 * q^19 - 1640 * q^20 - 786 * q^21 - 860 * q^22 - 1390 * q^23 - 865 * q^24 - 805 * q^25 - 843 * q^26 - 790 * q^27 - 876 * q^28 - 787 * q^29 - 908 * q^30 - 763 * q^31 - 848 * q^32 - 880 * q^33 - 1466 * q^34 - 849 * q^35 - 1015 * q^36 - 800 * q^37 - 887 * q^38 - 1710 * q^39 - 970 * q^40 - 843 * q^41 - 1007 * q^42 - 860 * q^43 - 940 * q^44 - 1574 * q^45 - 926 * q^46 - 818 * q^47 - 1067 * q^48 - 874 * q^49 - 962 * q^50 - 899 * q^51 - 939 * q^52 - 877 * q^53 - 1070 * q^54 - 920 * q^55 - 1686 * q^56 - 889 * q^57 - 1744 * q^58 - 854 * q^59 - 1206 * q^60 - 851 * q^61 - 1056 * q^62 - 985 * q^63 - 1133 * q^64 - 960 * q^65 - 1050 * q^66 - 1586 * q^67 - 1103 * q^68 - 996 * q^69 - 1125 * q^70 - 928 * q^71 - 1297 * q^72 - 925 * q^73 - 1051 * q^74 - 1034 * q^75 - 994 * q^76 - 1870 * q^77 - 1777 * q^78 - 1011 * q^79 - 1259 * q^80 - 1064 * q^81 - 1068 * q^82 - 964 * q^83 - 1357 * q^84 - 1041 * q^85 - 1024 * q^86 - 1093 * q^87 - 1120 * q^88 - 1530 * q^89 - 1368 * q^90 - 1049 * q^91 - 1170 * q^92 - 1095 * q^93 - 1178 * q^94 - 947 * q^95 - 2280 * q^96 - 996 * q^97 - 1198 * q^98 - 1080 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2299))\)

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
2299.2.a	\(\chi_{2299}(1, \cdot)\)	2299.2.a.a	1	1
		2299.2.a.b	1
		2299.2.a.c	1
		2299.2.a.d	1
		2299.2.a.e	2
		2299.2.a.f	2
		2299.2.a.g	2
		2299.2.a.h	2
		2299.2.a.i	2
		2299.2.a.j	2
		2299.2.a.k	2
		2299.2.a.l	3
		2299.2.a.m	3
		2299.2.a.n	5
		2299.2.a.o	7
		2299.2.a.p	7
		2299.2.a.q	7
		2299.2.a.r	7
		2299.2.a.s	7
		2299.2.a.t	14
		2299.2.a.u	14
		2299.2.a.v	16
		2299.2.a.w	16
		2299.2.a.x	20
		2299.2.a.y	20
2299.2.d	\(\chi_{2299}(2298, \cdot)\)	n/a	172	1
2299.2.e	\(\chi_{2299}(1090, \cdot)\)	n/a	344	2
2299.2.f	\(\chi_{2299}(856, \cdot)\)	n/a	648	4
2299.2.g	\(\chi_{2299}(483, \cdot)\)	n/a	344	2
2299.2.j	\(\chi_{2299}(606, \cdot)\)	n/a	1038	6
2299.2.k	\(\chi_{2299}(94, \cdot)\)	n/a	688	4
2299.2.n	\(\chi_{2299}(210, \cdot)\)	n/a	1980	10
2299.2.o	\(\chi_{2299}(372, \cdot)\)	n/a	1376	8
2299.2.q	\(\chi_{2299}(241, \cdot)\)	n/a	1032	6
2299.2.s	\(\chi_{2299}(208, \cdot)\)	n/a	2180	10
2299.2.x	\(\chi_{2299}(354, \cdot)\)	n/a	1376	8
2299.2.y	\(\chi_{2299}(45, \cdot)\)	n/a	4360	20
2299.2.z	\(\chi_{2299}(9, \cdot)\)	n/a	4128	24
2299.2.ba	\(\chi_{2299}(20, \cdot)\)	n/a	7920	40
2299.2.bd	\(\chi_{2299}(65, \cdot)\)	n/a	4360	20
2299.2.bf	\(\chi_{2299}(40, \cdot)\)	n/a	4128	24
2299.2.bh	\(\chi_{2299}(23, \cdot)\)	n/a	13080	60
2299.2.bk	\(\chi_{2299}(18, \cdot)\)	n/a	8720	40
2299.2.bl	\(\chi_{2299}(26, \cdot)\)	n/a	17440	80
2299.2.bn	\(\chi_{2299}(10, \cdot)\)	n/a	13080	60
2299.2.bp	\(\chi_{2299}(8, \cdot)\)	n/a	17440	80
2299.2.bs	\(\chi_{2299}(4, \cdot)\)	n/a	52320	240
2299.2.bu	\(\chi_{2299}(2, \cdot)\)	n/a	52320	240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2299))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2299)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 2}\)