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Properties

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

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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

\( 210638 q - 723 q^{2} - 721 q^{3} - 715 q^{4} - 717 q^{5} - 725 q^{6} - 733 q^{7} - 739 q^{8} - 743 q^{9} + O(q^{10}) \) \( 210638 q - 723 q^{2} - 721 q^{3} - 715 q^{4} - 717 q^{5} - 725 q^{6} - 733 q^{7} - 739 q^{8} - 743 q^{9} - 753 q^{10} - 810 q^{11} - 1405 q^{12} - 733 q^{13} - 759 q^{14} - 779 q^{15} - 823 q^{16} - 762 q^{17} - 807 q^{18} - 805 q^{19} - 1640 q^{20} - 786 q^{21} - 860 q^{22} - 1390 q^{23} - 865 q^{24} - 805 q^{25} - 843 q^{26} - 790 q^{27} - 876 q^{28} - 787 q^{29} - 908 q^{30} - 763 q^{31} - 848 q^{32} - 880 q^{33} - 1466 q^{34} - 849 q^{35} - 1015 q^{36} - 800 q^{37} - 887 q^{38} - 1710 q^{39} - 970 q^{40} - 843 q^{41} - 1007 q^{42} - 860 q^{43} - 940 q^{44} - 1574 q^{45} - 926 q^{46} - 818 q^{47} - 1067 q^{48} - 874 q^{49} - 962 q^{50} - 899 q^{51} - 939 q^{52} - 877 q^{53} - 1070 q^{54} - 920 q^{55} - 1686 q^{56} - 889 q^{57} - 1744 q^{58} - 854 q^{59} - 1206 q^{60} - 851 q^{61} - 1056 q^{62} - 985 q^{63} - 1133 q^{64} - 960 q^{65} - 1050 q^{66} - 1586 q^{67} - 1103 q^{68} - 996 q^{69} - 1125 q^{70} - 928 q^{71} - 1297 q^{72} - 925 q^{73} - 1051 q^{74} - 1034 q^{75} - 994 q^{76} - 1870 q^{77} - 1777 q^{78} - 1011 q^{79} - 1259 q^{80} - 1064 q^{81} - 1068 q^{82} - 964 q^{83} - 1357 q^{84} - 1041 q^{85} - 1024 q^{86} - 1093 q^{87} - 1120 q^{88} - 1530 q^{89} - 1368 q^{90} - 1049 q^{91} - 1170 q^{92} - 1095 q^{93} - 1178 q^{94} - 947 q^{95} - 2280 q^{96} - 996 q^{97} - 1198 q^{98} - 1080 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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