Properties

Label 1849.2
Level 1849
Weight 2
Dimension 140916
Nonzero newspaces 8
Sturm bound 569492
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1849 = 43^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(569492\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1849))\).

Total New Old
Modular forms 143717 143521 196
Cusp forms 141030 140916 114
Eisenstein series 2687 2605 82

Trace form

\( 140916 q - 864 q^{2} - 865 q^{3} - 868 q^{4} - 867 q^{5} - 873 q^{6} - 869 q^{7} - 876 q^{8} - 874 q^{9} + O(q^{10}) \) \( 140916 q - 864 q^{2} - 865 q^{3} - 868 q^{4} - 867 q^{5} - 873 q^{6} - 869 q^{7} - 876 q^{8} - 874 q^{9} - 879 q^{10} - 873 q^{11} - 889 q^{12} - 875 q^{13} - 885 q^{14} - 885 q^{15} - 892 q^{16} - 879 q^{17} - 900 q^{18} - 881 q^{19} - 903 q^{20} - 893 q^{21} - 897 q^{22} - 885 q^{23} - 921 q^{24} - 892 q^{25} - 903 q^{26} - 901 q^{27} - 917 q^{28} - 891 q^{29} - 933 q^{30} - 879 q^{31} - 840 q^{32} - 825 q^{33} - 789 q^{34} - 825 q^{35} - 728 q^{36} - 815 q^{37} - 753 q^{38} - 819 q^{39} - 615 q^{40} - 861 q^{41} - 747 q^{42} - 777 q^{43} - 1617 q^{44} - 729 q^{45} - 765 q^{46} - 867 q^{47} - 649 q^{48} - 820 q^{49} - 786 q^{50} - 849 q^{51} - 735 q^{52} - 831 q^{53} - 855 q^{54} - 849 q^{55} - 897 q^{56} - 927 q^{57} - 951 q^{58} - 921 q^{59} - 1029 q^{60} - 923 q^{61} - 957 q^{62} - 965 q^{63} - 988 q^{64} - 945 q^{65} - 1005 q^{66} - 929 q^{67} - 987 q^{68} - 873 q^{69} - 837 q^{70} - 849 q^{71} - 636 q^{72} - 851 q^{73} - 681 q^{74} - 691 q^{75} - 707 q^{76} - 705 q^{77} - 483 q^{78} - 773 q^{79} - 711 q^{80} - 646 q^{81} - 567 q^{82} - 777 q^{83} - 245 q^{84} - 759 q^{85} - 714 q^{86} - 1401 q^{87} - 621 q^{88} - 783 q^{89} - 339 q^{90} - 805 q^{91} - 609 q^{92} - 653 q^{93} - 669 q^{94} - 813 q^{95} - 567 q^{96} - 707 q^{97} - 738 q^{98} - 723 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1849))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1849.2.a \(\chi_{1849}(1, \cdot)\) 1849.2.a.a 1 1
1849.2.a.b 1
1849.2.a.c 1
1849.2.a.d 1
1849.2.a.e 2
1849.2.a.f 2
1849.2.a.g 2
1849.2.a.h 2
1849.2.a.i 3
1849.2.a.j 3
1849.2.a.k 3
1849.2.a.l 3
1849.2.a.m 10
1849.2.a.n 18
1849.2.a.o 18
1849.2.a.p 20
1849.2.a.q 20
1849.2.a.r 20
1849.2.c \(\chi_{1849}(423, \cdot)\) n/a 260 2
1849.2.e \(\chi_{1849}(78, \cdot)\) n/a 786 6
1849.2.g \(\chi_{1849}(210, \cdot)\) n/a 1560 12
1849.2.i \(\chi_{1849}(44, \cdot)\) n/a 6552 42
1849.2.k \(\chi_{1849}(6, \cdot)\) n/a 13188 84
1849.2.m \(\chi_{1849}(4, \cdot)\) n/a 39312 252
1849.2.o \(\chi_{1849}(9, \cdot)\) n/a 79128 504

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1849))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1849)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 2}\)