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Properties

Label 286.2
Level 286
Weight 2
Dimension 819
Nonzero newspaces 12
Newform subspaces 34
Sturm bound 10080
Trace bound 4

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Defining parameters

Level: \( N \) = \( 286 = 2 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 34 \)
Sturm bound: \(10080\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(286))\).

Total New Old
Modular forms 2760 819 1941
Cusp forms 2281 819 1462
Eisenstein series 479 0 479

Trace form

\( 819 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 33 q^{9} + O(q^{10}) \) \( 819 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 33 q^{9} - 32 q^{10} - 9 q^{11} - 16 q^{12} - 31 q^{13} - 20 q^{14} - 36 q^{15} - 5 q^{16} - 16 q^{17} - q^{18} - 26 q^{19} + 12 q^{20} + 23 q^{22} + 8 q^{23} + 2 q^{24} - 17 q^{25} + 7 q^{26} - 42 q^{27} - 4 q^{28} - 68 q^{29} - 36 q^{30} - 44 q^{31} - 7 q^{32} - 78 q^{33} - 34 q^{34} - 120 q^{35} - 19 q^{36} + 12 q^{37} - 72 q^{38} - 46 q^{39} - 2 q^{40} - 56 q^{41} - 36 q^{42} - 56 q^{43} - 31 q^{44} - 16 q^{45} - 16 q^{46} - 32 q^{47} + 12 q^{48} - 13 q^{49} - q^{50} - 58 q^{51} - 7 q^{52} - 10 q^{53} - 32 q^{54} - 62 q^{55} - 58 q^{57} - 44 q^{58} - 46 q^{59} - 16 q^{60} - 32 q^{61} - 36 q^{62} - 176 q^{63} - 3 q^{64} - 112 q^{65} - 76 q^{66} - 128 q^{67} + 8 q^{68} - 172 q^{69} - 8 q^{70} - 88 q^{71} - 49 q^{72} - 74 q^{73} - 4 q^{74} - 154 q^{75} - 16 q^{76} - 96 q^{77} - 52 q^{78} - 52 q^{79} - 8 q^{80} - 155 q^{81} - 46 q^{82} - 70 q^{83} - 40 q^{84} - 142 q^{85} - 46 q^{86} - 80 q^{87} + 3 q^{88} - 82 q^{89} - 66 q^{90} - 36 q^{91} - 36 q^{92} - 100 q^{93} - 96 q^{94} - 4 q^{95} + 12 q^{96} - 96 q^{97} - 15 q^{98} - 69 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)

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
286.2.a \(\chi_{286}(1, \cdot)\) 286.2.a.a 1 1
286.2.a.b 1
286.2.a.c 1
286.2.a.d 1
286.2.a.e 1
286.2.a.f 1
286.2.a.g 3
286.2.b \(\chi_{286}(155, \cdot)\) 286.2.b.a 2 1
286.2.b.b 2
286.2.b.c 2
286.2.b.d 4
286.2.e \(\chi_{286}(133, \cdot)\) 286.2.e.a 2 2
286.2.e.b 2
286.2.e.c 2
286.2.e.d 2
286.2.e.e 4
286.2.e.f 6
286.2.e.g 6
286.2.g \(\chi_{286}(21, \cdot)\) 286.2.g.a 28 2
286.2.h \(\chi_{286}(27, \cdot)\) 286.2.h.a 4 4
286.2.h.b 8
286.2.h.c 12
286.2.h.d 12
286.2.h.e 12
286.2.j \(\chi_{286}(23, \cdot)\) 286.2.j.a 12 2
286.2.j.b 16
286.2.n \(\chi_{286}(25, \cdot)\) 286.2.n.a 8 4
286.2.n.b 48
286.2.o \(\chi_{286}(175, \cdot)\) 286.2.o.a 56 4
286.2.q \(\chi_{286}(3, \cdot)\) 286.2.q.a 56 8
286.2.q.b 56
286.2.r \(\chi_{286}(57, \cdot)\) 286.2.r.a 112 8
286.2.u \(\chi_{286}(49, \cdot)\) 286.2.u.a 112 8
286.2.x \(\chi_{286}(7, \cdot)\) 286.2.x.a 224 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(286))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(286)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 2}\)