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Properties

Label 2011.2
Level 2011
Weight 2
Dimension 167501
Nonzero newspaces 8
Sturm bound 674020
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2011 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(674020\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2011))\).

Total New Old
Modular forms 169510 169510 0
Cusp forms 167501 167501 0
Eisenstein series 2009 2009 0

Trace form

\( 167501 q - 1002 q^{2} - 1001 q^{3} - 998 q^{4} - 999 q^{5} - 993 q^{6} - 997 q^{7} - 990 q^{8} - 992 q^{9} + O(q^{10}) \) \( 167501 q - 1002 q^{2} - 1001 q^{3} - 998 q^{4} - 999 q^{5} - 993 q^{6} - 997 q^{7} - 990 q^{8} - 992 q^{9} - 987 q^{10} - 993 q^{11} - 977 q^{12} - 991 q^{13} - 981 q^{14} - 981 q^{15} - 974 q^{16} - 987 q^{17} - 966 q^{18} - 985 q^{19} - 963 q^{20} - 973 q^{21} - 969 q^{22} - 981 q^{23} - 945 q^{24} - 974 q^{25} - 963 q^{26} - 965 q^{27} - 949 q^{28} - 975 q^{29} - 933 q^{30} - 973 q^{31} - 942 q^{32} - 957 q^{33} - 951 q^{34} - 957 q^{35} - 914 q^{36} - 967 q^{37} - 945 q^{38} - 949 q^{39} - 915 q^{40} - 963 q^{41} - 909 q^{42} - 961 q^{43} - 921 q^{44} - 927 q^{45} - 933 q^{46} - 957 q^{47} - 881 q^{48} - 948 q^{49} - 912 q^{50} - 933 q^{51} - 907 q^{52} - 951 q^{53} - 885 q^{54} - 933 q^{55} - 885 q^{56} - 925 q^{57} - 915 q^{58} - 945 q^{59} - 837 q^{60} - 943 q^{61} - 909 q^{62} - 901 q^{63} - 878 q^{64} - 921 q^{65} - 861 q^{66} - 937 q^{67} - 879 q^{68} - 909 q^{69} - 861 q^{70} - 933 q^{71} - 810 q^{72} - 931 q^{73} - 891 q^{74} - 881 q^{75} - 865 q^{76} - 909 q^{77} - 837 q^{78} - 925 q^{79} - 819 q^{80} - 884 q^{81} - 879 q^{82} - 921 q^{83} - 781 q^{84} - 897 q^{85} - 873 q^{86} - 885 q^{87} - 825 q^{88} - 915 q^{89} - 771 q^{90} - 893 q^{91} - 837 q^{92} - 877 q^{93} - 861 q^{94} - 885 q^{95} - 753 q^{96} - 907 q^{97} - 834 q^{98} - 849 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2011))\)

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
2011.2.a \(\chi_{2011}(1, \cdot)\) 2011.2.a.a 77 1
2011.2.a.b 90
2011.2.c \(\chi_{2011}(205, \cdot)\) n/a 334 2
2011.2.d \(\chi_{2011}(798, \cdot)\) n/a 664 4
2011.2.g \(\chi_{2011}(514, \cdot)\) n/a 1336 8
2011.2.i \(\chi_{2011}(64, \cdot)\) n/a 10956 66
2011.2.k \(\chi_{2011}(4, \cdot)\) n/a 22044 132
2011.2.l \(\chi_{2011}(6, \cdot)\) n/a 43824 264
2011.2.o \(\chi_{2011}(5, \cdot)\) n/a 88176 528

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