Properties

Label 1338.2
Level 1338
Weight 2
Dimension 12433
Nonzero newspaces 8
Sturm bound 198912
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1338 = 2 \cdot 3 \cdot 223 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(198912\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1338))\).

Total New Old
Modular forms 50616 12433 38183
Cusp forms 48841 12433 36408
Eisenstein series 1775 0 1775

Trace form

\( 12433 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 12433 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + 14 q^{13} + 8 q^{14} + 6 q^{15} + q^{16} + 18 q^{17} + q^{18} + 20 q^{19} + 6 q^{20} + 8 q^{21} + 12 q^{22} + 24 q^{23} + q^{24} + 31 q^{25} + 14 q^{26} + q^{27} + 8 q^{28} + 30 q^{29} + 6 q^{30} + 32 q^{31} + q^{32} + 12 q^{33} + 18 q^{34} + 48 q^{35} + q^{36} + 38 q^{37} + 20 q^{38} + 14 q^{39} + 6 q^{40} + 42 q^{41} + 8 q^{42} + 44 q^{43} + 12 q^{44} + 6 q^{45} + 24 q^{46} + 48 q^{47} + q^{48} + 57 q^{49} + 31 q^{50} + 18 q^{51} + 14 q^{52} + 54 q^{53} + q^{54} + 72 q^{55} + 8 q^{56} + 20 q^{57} + 30 q^{58} + 60 q^{59} + 6 q^{60} + 62 q^{61} + 32 q^{62} + 8 q^{63} + q^{64} + 84 q^{65} + 12 q^{66} + 68 q^{67} + 18 q^{68} + 24 q^{69} + 48 q^{70} + 72 q^{71} + q^{72} + 74 q^{73} + 38 q^{74} + 31 q^{75} + 20 q^{76} + 96 q^{77} + 14 q^{78} + 80 q^{79} + 6 q^{80} + q^{81} + 42 q^{82} + 84 q^{83} + 8 q^{84} + 108 q^{85} + 44 q^{86} + 30 q^{87} + 12 q^{88} + 90 q^{89} + 6 q^{90} + 112 q^{91} + 24 q^{92} + 32 q^{93} + 48 q^{94} + 120 q^{95} + q^{96} + 98 q^{97} + 57 q^{98} + 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1338))\)

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
1338.2.a \(\chi_{1338}(1, \cdot)\) 1338.2.a.a 1 1
1338.2.a.b 2
1338.2.a.c 3
1338.2.a.d 3
1338.2.a.e 3
1338.2.a.f 3
1338.2.a.g 4
1338.2.a.h 5
1338.2.a.i 6
1338.2.a.j 7
1338.2.d \(\chi_{1338}(1337, \cdot)\) 1338.2.d.a 76 1
1338.2.e \(\chi_{1338}(931, \cdot)\) 1338.2.e.a 2 2
1338.2.e.b 2
1338.2.e.c 2
1338.2.e.d 4
1338.2.e.e 4
1338.2.e.f 4
1338.2.e.g 12
1338.2.e.h 14
1338.2.e.i 14
1338.2.e.j 18
1338.2.f \(\chi_{1338}(263, \cdot)\) n/a 148 2
1338.2.i \(\chi_{1338}(7, \cdot)\) n/a 1296 36
1338.2.j \(\chi_{1338}(59, \cdot)\) n/a 2736 36
1338.2.m \(\chi_{1338}(19, \cdot)\) n/a 2736 72
1338.2.p \(\chi_{1338}(5, \cdot)\) n/a 5328 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1338))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1338)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(446))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(669))\)\(^{\oplus 2}\)