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Properties

Label 1931.2
Level 1931
Weight 2
Dimension 154401
Nonzero newspaces 4
Sturm bound 621460
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1931 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(621460\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1931))\).

Total New Old
Modular forms 156330 156330 0
Cusp forms 154401 154401 0
Eisenstein series 1929 1929 0

Trace form

\( 154401 q - 962 q^{2} - 961 q^{3} - 958 q^{4} - 959 q^{5} - 953 q^{6} - 957 q^{7} - 950 q^{8} - 952 q^{9} + O(q^{10}) \) \( 154401 q - 962 q^{2} - 961 q^{3} - 958 q^{4} - 959 q^{5} - 953 q^{6} - 957 q^{7} - 950 q^{8} - 952 q^{9} - 947 q^{10} - 953 q^{11} - 937 q^{12} - 951 q^{13} - 941 q^{14} - 941 q^{15} - 934 q^{16} - 947 q^{17} - 926 q^{18} - 945 q^{19} - 923 q^{20} - 933 q^{21} - 929 q^{22} - 941 q^{23} - 905 q^{24} - 934 q^{25} - 923 q^{26} - 925 q^{27} - 909 q^{28} - 935 q^{29} - 893 q^{30} - 933 q^{31} - 902 q^{32} - 917 q^{33} - 911 q^{34} - 917 q^{35} - 874 q^{36} - 927 q^{37} - 905 q^{38} - 909 q^{39} - 875 q^{40} - 923 q^{41} - 869 q^{42} - 921 q^{43} - 881 q^{44} - 887 q^{45} - 893 q^{46} - 917 q^{47} - 841 q^{48} - 908 q^{49} - 872 q^{50} - 893 q^{51} - 867 q^{52} - 911 q^{53} - 845 q^{54} - 893 q^{55} - 845 q^{56} - 885 q^{57} - 875 q^{58} - 905 q^{59} - 797 q^{60} - 903 q^{61} - 869 q^{62} - 861 q^{63} - 838 q^{64} - 881 q^{65} - 821 q^{66} - 897 q^{67} - 839 q^{68} - 869 q^{69} - 821 q^{70} - 893 q^{71} - 770 q^{72} - 891 q^{73} - 851 q^{74} - 841 q^{75} - 825 q^{76} - 869 q^{77} - 797 q^{78} - 885 q^{79} - 779 q^{80} - 844 q^{81} - 839 q^{82} - 881 q^{83} - 741 q^{84} - 857 q^{85} - 833 q^{86} - 845 q^{87} - 785 q^{88} - 875 q^{89} - 731 q^{90} - 853 q^{91} - 797 q^{92} - 837 q^{93} - 821 q^{94} - 845 q^{95} - 713 q^{96} - 867 q^{97} - 794 q^{98} - 809 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1931))\)

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
1931.2.a \(\chi_{1931}(1, \cdot)\) 1931.2.a.a 60 1
1931.2.a.b 101
1931.2.c \(\chi_{1931}(1101, \cdot)\) n/a 640 4
1931.2.e \(\chi_{1931}(11, \cdot)\) n/a 30720 192
1931.2.g \(\chi_{1931}(3, \cdot)\) n/a 122880 768

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