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Properties

Label 387.2
Level 387
Weight 2
Dimension 4200
Nonzero newspaces 20
Newform subspaces 48
Sturm bound 22176
Trace bound 5

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Defining parameters

Level: \( N \) = \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 48 \)
Sturm bound: \(22176\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(387))\).

Total New Old
Modular forms 5880 4568 1312
Cusp forms 5209 4200 1009
Eisenstein series 671 368 303

Trace form

\( 4200 q - 63 q^{2} - 84 q^{3} - 63 q^{4} - 63 q^{5} - 84 q^{6} - 63 q^{7} - 63 q^{8} - 84 q^{9} + O(q^{10}) \) \( 4200 q - 63 q^{2} - 84 q^{3} - 63 q^{4} - 63 q^{5} - 84 q^{6} - 63 q^{7} - 63 q^{8} - 84 q^{9} - 189 q^{10} - 63 q^{11} - 84 q^{12} - 63 q^{13} - 63 q^{14} - 84 q^{15} - 63 q^{16} - 63 q^{17} - 84 q^{18} - 189 q^{19} - 63 q^{20} - 84 q^{21} - 63 q^{22} - 63 q^{23} - 84 q^{24} - 63 q^{25} - 63 q^{26} - 84 q^{27} - 189 q^{28} - 63 q^{29} - 84 q^{30} - 70 q^{31} - 105 q^{32} - 84 q^{33} - 126 q^{34} - 105 q^{35} - 84 q^{36} - 231 q^{37} - 147 q^{38} - 84 q^{39} - 231 q^{40} - 84 q^{41} - 84 q^{42} - 168 q^{43} - 210 q^{44} - 84 q^{45} - 273 q^{46} - 84 q^{47} - 84 q^{48} - 112 q^{49} - 147 q^{50} - 84 q^{51} - 175 q^{52} - 105 q^{53} - 84 q^{54} - 231 q^{55} - 105 q^{56} - 84 q^{57} - 63 q^{58} - 63 q^{59} - 84 q^{60} - 63 q^{61} - 63 q^{62} - 84 q^{63} - 189 q^{64} - 63 q^{65} - 84 q^{66} - 63 q^{67} - 63 q^{68} - 84 q^{69} - 147 q^{70} - 105 q^{71} - 84 q^{72} - 231 q^{73} - 210 q^{74} - 84 q^{75} - 210 q^{76} - 189 q^{77} - 84 q^{78} - 147 q^{79} - 231 q^{80} - 84 q^{81} - 399 q^{82} - 147 q^{83} - 168 q^{85} - 231 q^{86} - 168 q^{87} - 273 q^{88} - 147 q^{89} - 84 q^{90} - 273 q^{91} - 273 q^{92} - 84 q^{93} - 231 q^{94} - 147 q^{95} - 84 q^{96} - 189 q^{97} - 210 q^{98} - 84 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(387))\)

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
387.2.a \(\chi_{387}(1, \cdot)\) 387.2.a.a 1 1
387.2.a.b 1
387.2.a.c 1
387.2.a.d 1
387.2.a.e 1
387.2.a.f 2
387.2.a.g 2
387.2.a.h 2
387.2.a.i 3
387.2.a.j 4
387.2.d \(\chi_{387}(386, \cdot)\) 387.2.d.a 4 1
387.2.d.b 12
387.2.e \(\chi_{387}(49, \cdot)\) 387.2.e.a 84 2
387.2.f \(\chi_{387}(130, \cdot)\) 387.2.f.a 2 2
387.2.f.b 4
387.2.f.c 38
387.2.f.d 40
387.2.g \(\chi_{387}(178, \cdot)\) 387.2.g.a 84 2
387.2.h \(\chi_{387}(208, \cdot)\) 387.2.h.a 2 2
387.2.h.b 2
387.2.h.c 2
387.2.h.d 4
387.2.h.e 6
387.2.h.f 6
387.2.h.g 12
387.2.k \(\chi_{387}(308, \cdot)\) 387.2.k.a 84 2
387.2.l \(\chi_{387}(128, \cdot)\) 387.2.l.a 84 2
387.2.m \(\chi_{387}(50, \cdot)\) 387.2.m.a 84 2
387.2.t \(\chi_{387}(80, \cdot)\) 387.2.t.a 28 2
387.2.u \(\chi_{387}(64, \cdot)\) 387.2.u.a 6 6
387.2.u.b 6
387.2.u.c 6
387.2.u.d 12
387.2.u.e 30
387.2.u.f 48
387.2.v \(\chi_{387}(8, \cdot)\) 387.2.v.a 96 6
387.2.y \(\chi_{387}(10, \cdot)\) 387.2.y.a 12 12
387.2.y.b 36
387.2.y.c 36
387.2.y.d 48
387.2.y.e 72
387.2.z \(\chi_{387}(13, \cdot)\) 387.2.z.a 504 12
387.2.ba \(\chi_{387}(4, \cdot)\) 387.2.ba.a 504 12
387.2.bb \(\chi_{387}(25, \cdot)\) 387.2.bb.a 504 12
387.2.bc \(\chi_{387}(26, \cdot)\) 387.2.bc.a 168 12
387.2.bj \(\chi_{387}(20, \cdot)\) 387.2.bj.a 504 12
387.2.bk \(\chi_{387}(2, \cdot)\) 387.2.bk.a 504 12
387.2.bl \(\chi_{387}(5, \cdot)\) 387.2.bl.a 504 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(387))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(387)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(387))\)\(^{\oplus 1}\)