Properties

Label 3017.2
Level 3017
Weight 2
Dimension 353889
Nonzero newspaces 16
Sturm bound 1486080
Trace bound 2

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Defining parameters

Level: \( N \) = \( 3017 = 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(1486080\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3017))\).

Total New Old
Modular forms 374100 358181 15919
Cusp forms 368941 353889 15052
Eisenstein series 5159 4292 867

Trace form

\( 353889 q - 863 q^{2} - 864 q^{3} - 867 q^{4} - 866 q^{5} - 872 q^{6} - 1076 q^{7} - 2165 q^{8} - 873 q^{9} + O(q^{10}) \) \( 353889 q - 863 q^{2} - 864 q^{3} - 867 q^{4} - 866 q^{5} - 872 q^{6} - 1076 q^{7} - 2165 q^{8} - 873 q^{9} - 878 q^{10} - 872 q^{11} - 888 q^{12} - 874 q^{13} - 1078 q^{14} - 2174 q^{15} - 891 q^{16} - 878 q^{17} - 899 q^{18} - 880 q^{19} - 902 q^{20} - 1079 q^{21} - 2186 q^{22} - 884 q^{23} - 920 q^{24} - 891 q^{25} - 902 q^{26} - 900 q^{27} - 1082 q^{28} - 2180 q^{29} - 932 q^{30} - 892 q^{31} - 923 q^{32} - 908 q^{33} - 914 q^{34} - 1081 q^{35} - 2241 q^{36} - 898 q^{37} - 920 q^{38} - 916 q^{39} - 950 q^{40} - 902 q^{41} - 1087 q^{42} - 2194 q^{43} - 944 q^{44} - 938 q^{45} - 932 q^{46} - 908 q^{47} - 984 q^{48} - 1076 q^{49} - 2243 q^{50} - 932 q^{51} - 958 q^{52} - 914 q^{53} - 980 q^{54} - 932 q^{55} - 1090 q^{56} - 2230 q^{57} - 950 q^{58} - 920 q^{59} - 1028 q^{60} - 922 q^{61} - 956 q^{62} - 1088 q^{63} - 2277 q^{64} - 944 q^{65} - 1004 q^{66} - 928 q^{67} - 986 q^{68} - 956 q^{69} - 1093 q^{70} - 2222 q^{71} - 1055 q^{72} - 934 q^{73} - 974 q^{74} - 984 q^{75} - 1000 q^{76} - 1087 q^{77} - 2318 q^{78} - 940 q^{79} - 1046 q^{80} - 981 q^{81} - 986 q^{82} - 944 q^{83} - 1103 q^{84} - 2258 q^{85} - 992 q^{86} - 980 q^{87} - 1040 q^{88} - 950 q^{89} - 1094 q^{90} - 1089 q^{91} - 2318 q^{92} - 988 q^{93} - 1004 q^{94} - 980 q^{95} - 1112 q^{96} - 958 q^{97} - 1078 q^{98} - 2306 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3017))\)

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
3017.2.a \(\chi_{3017}(1, \cdot)\) 3017.2.a.a 1 1
3017.2.a.b 1
3017.2.a.c 37
3017.2.a.d 48
3017.2.a.e 58
3017.2.a.f 70
3017.2.c \(\chi_{3017}(3016, \cdot)\) n/a 286 1
3017.2.e \(\chi_{3017}(863, \cdot)\) n/a 572 2
3017.2.f \(\chi_{3017}(526, \cdot)\) n/a 864 4
3017.2.i \(\chi_{3017}(430, \cdot)\) n/a 572 2
3017.2.j \(\chi_{3017}(888, \cdot)\) n/a 1144 4
3017.2.m \(\chi_{3017}(95, \cdot)\) n/a 2288 8
3017.2.o \(\chi_{3017}(26, \cdot)\) n/a 2288 8
3017.2.q \(\chi_{3017}(8, \cdot)\) n/a 9072 42
3017.2.s \(\chi_{3017}(188, \cdot)\) n/a 12012 42
3017.2.u \(\chi_{3017}(2, \cdot)\) n/a 24024 84
3017.2.v \(\chi_{3017}(15, \cdot)\) n/a 36288 168
3017.2.w \(\chi_{3017}(47, \cdot)\) n/a 24024 84
3017.2.bb \(\chi_{3017}(13, \cdot)\) n/a 48048 168
3017.2.bc \(\chi_{3017}(11, \cdot)\) n/a 96096 336
3017.2.be \(\chi_{3017}(17, \cdot)\) n/a 96096 336

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3017))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3017)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(431))\)\(^{\oplus 2}\)