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Properties

Label 762.2
Level 762
Weight 2
Dimension 4033
Nonzero newspaces 12
Newform subspaces 46
Sturm bound 64512
Trace bound 1

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Defining parameters

Level: \( N \) = \( 762 = 2 \cdot 3 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 46 \)
Sturm bound: \(64512\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(762))\).

Total New Old
Modular forms 16632 4033 12599
Cusp forms 15625 4033 11592
Eisenstein series 1007 0 1007

Trace form

\( 4033 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 4033 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + 14 q^{13} + 8 q^{14} + 6 q^{15} + q^{16} + 18 q^{17} + q^{18} + 20 q^{19} + 6 q^{20} + 8 q^{21} + 12 q^{22} + 24 q^{23} + q^{24} + 31 q^{25} + 14 q^{26} + q^{27} + 8 q^{28} + 30 q^{29} + 6 q^{30} + 32 q^{31} + q^{32} + 12 q^{33} + 18 q^{34} + 48 q^{35} + q^{36} + 38 q^{37} + 20 q^{38} + 14 q^{39} + 6 q^{40} + 42 q^{41} + 8 q^{42} + 44 q^{43} + 12 q^{44} + 6 q^{45} + 24 q^{46} + 48 q^{47} + q^{48} + 57 q^{49} + 31 q^{50} + 18 q^{51} + 14 q^{52} + 54 q^{53} + q^{54} + 72 q^{55} + 8 q^{56} + 20 q^{57} + 30 q^{58} + 60 q^{59} + 6 q^{60} + 62 q^{61} + 32 q^{62} + 8 q^{63} + q^{64} + 84 q^{65} + 12 q^{66} + 68 q^{67} + 18 q^{68} + 24 q^{69} + 48 q^{70} + 72 q^{71} + q^{72} + 74 q^{73} + 38 q^{74} + 31 q^{75} + 20 q^{76} + 96 q^{77} + 14 q^{78} + 80 q^{79} + 6 q^{80} + q^{81} + 42 q^{82} + 84 q^{83} + 8 q^{84} + 108 q^{85} + 44 q^{86} + 30 q^{87} + 12 q^{88} + 90 q^{89} + 6 q^{90} + 112 q^{91} + 24 q^{92} + 32 q^{93} + 48 q^{94} + 120 q^{95} + q^{96} + 98 q^{97} + 57 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(762))\)

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
762.2.a \(\chi_{762}(1, \cdot)\) 762.2.a.a 1 1
762.2.a.b 1
762.2.a.c 1
762.2.a.d 1
762.2.a.e 1
762.2.a.f 1
762.2.a.g 1
762.2.a.h 2
762.2.a.i 2
762.2.a.j 2
762.2.a.k 3
762.2.a.l 5
762.2.d \(\chi_{762}(761, \cdot)\) 762.2.d.a 44 1
762.2.e \(\chi_{762}(19, \cdot)\) 762.2.e.a 2 2
762.2.e.b 4
762.2.e.c 4
762.2.e.d 4
762.2.e.e 4
762.2.e.f 6
762.2.e.g 6
762.2.e.h 10
762.2.h \(\chi_{762}(401, \cdot)\) 762.2.h.a 4 2
762.2.h.b 84
762.2.i \(\chi_{762}(385, \cdot)\) 762.2.i.a 6 6
762.2.i.b 24
762.2.i.c 24
762.2.i.d 30
762.2.i.e 36
762.2.j \(\chi_{762}(37, \cdot)\) 762.2.j.a 12 6
762.2.j.b 18
762.2.j.c 30
762.2.j.d 36
762.2.j.e 36
762.2.k \(\chi_{762}(95, \cdot)\) 762.2.k.a 264 6
762.2.n \(\chi_{762}(59, \cdot)\) 762.2.n.a 252 6
762.2.q \(\chi_{762}(25, \cdot)\) 762.2.q.a 12 12
762.2.q.b 36
762.2.q.c 60
762.2.q.d 60
762.2.q.e 72
762.2.r \(\chi_{762}(5, \cdot)\) 762.2.r.a 528 12
762.2.u \(\chi_{762}(13, \cdot)\) 762.2.u.a 180 36
762.2.u.b 180
762.2.u.c 216
762.2.u.d 216
762.2.x \(\chi_{762}(23, \cdot)\) 762.2.x.a 1512 36

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(762))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(762)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(127))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(254))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(381))\)\(^{\oplus 2}\)