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Properties

Label 387.3
Level 387
Weight 3
Dimension 8585
Nonzero newspaces 20
Newform subspaces 36
Sturm bound 33264
Trace bound 5

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Defining parameters

Level: \( N \) = \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 36 \)
Sturm bound: \(33264\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(387))\).

Total New Old
Modular forms 11424 8955 2469
Cusp forms 10752 8585 2167
Eisenstein series 672 370 302

Trace form

\( 8585 q - 57 q^{2} - 78 q^{3} - 61 q^{4} - 75 q^{5} - 102 q^{6} - 59 q^{7} - 63 q^{8} - 66 q^{9} + O(q^{10}) \) \( 8585 q - 57 q^{2} - 78 q^{3} - 61 q^{4} - 75 q^{5} - 102 q^{6} - 59 q^{7} - 63 q^{8} - 66 q^{9} - 165 q^{10} - 57 q^{11} - 96 q^{12} - 71 q^{13} - 75 q^{14} - 84 q^{15} - 85 q^{16} - 63 q^{17} - 84 q^{18} - 233 q^{19} - 51 q^{20} - 72 q^{21} - 69 q^{22} + 33 q^{23} + 6 q^{24} - 37 q^{25} - 63 q^{26} - 192 q^{27} - 197 q^{28} - 219 q^{29} - 120 q^{30} + 78 q^{31} + 303 q^{32} - 102 q^{33} + 495 q^{34} + 231 q^{35} - 66 q^{36} + 157 q^{37} + 339 q^{38} - 36 q^{39} + 213 q^{40} - 84 q^{42} - 229 q^{43} - 294 q^{44} + 24 q^{45} - 717 q^{46} - 150 q^{48} - 496 q^{49} - 813 q^{50} - 246 q^{51} - 1191 q^{52} - 525 q^{53} + 78 q^{54} - 711 q^{55} - 591 q^{56} - 18 q^{57} + 93 q^{58} - 237 q^{59} - 120 q^{60} + 49 q^{61} - 63 q^{62} - 156 q^{63} + 95 q^{64} - 111 q^{65} - 48 q^{66} - 125 q^{67} - 9 q^{68} - 84 q^{69} + 1173 q^{70} + 525 q^{71} - 354 q^{72} + 55 q^{73} + 1350 q^{74} - 6 q^{75} + 1282 q^{76} + 933 q^{77} - 156 q^{78} + 517 q^{79} + 777 q^{80} + 78 q^{81} + 357 q^{82} + 273 q^{83} - 240 q^{84} + 66 q^{85} - 48 q^{86} + 300 q^{87} - 681 q^{88} - 399 q^{89} - 192 q^{90} - 661 q^{91} - 1629 q^{92} - 468 q^{93} - 1743 q^{94} - 1035 q^{95} - 84 q^{96} - 1805 q^{97} - 1974 q^{98} - 84 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(387))\)

We only show spaces with odd 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
387.3.b \(\chi_{387}(343, \cdot)\) 387.3.b.a 1 1
387.3.b.b 2
387.3.b.c 6
387.3.b.d 12
387.3.b.e 14
387.3.c \(\chi_{387}(44, \cdot)\) 387.3.c.a 28 1
387.3.i \(\chi_{387}(251, \cdot)\) 387.3.i.a 60 2
387.3.j \(\chi_{387}(37, \cdot)\) 387.3.j.a 2 2
387.3.j.b 2
387.3.j.c 12
387.3.j.d 14
387.3.j.e 14
387.3.j.f 28
387.3.n \(\chi_{387}(265, \cdot)\) 387.3.n.a 172 2
387.3.o \(\chi_{387}(92, \cdot)\) 387.3.o.a 172 2
387.3.p \(\chi_{387}(221, \cdot)\) 387.3.p.a 172 2
387.3.q \(\chi_{387}(173, \cdot)\) 387.3.q.a 168 2
387.3.r \(\chi_{387}(7, \cdot)\) 387.3.r.a 172 2
387.3.s \(\chi_{387}(85, \cdot)\) 387.3.s.a 172 2
387.3.w \(\chi_{387}(82, \cdot)\) 387.3.w.a 12 6
387.3.w.b 42
387.3.w.c 72
387.3.w.d 84
387.3.x \(\chi_{387}(35, \cdot)\) 387.3.x.a 168 6
387.3.bd \(\chi_{387}(11, \cdot)\) 387.3.bd.a 1032 12
387.3.be \(\chi_{387}(23, \cdot)\) 387.3.be.a 1032 12
387.3.bf \(\chi_{387}(22, \cdot)\) 387.3.bf.a 1032 12
387.3.bg \(\chi_{387}(34, \cdot)\) 387.3.bg.a 1032 12
387.3.bh \(\chi_{387}(106, \cdot)\) 387.3.bh.a 1032 12
387.3.bi \(\chi_{387}(14, \cdot)\) 387.3.bi.a 1032 12
387.3.bm \(\chi_{387}(17, \cdot)\) 387.3.bm.a 360 12
387.3.bn \(\chi_{387}(19, \cdot)\) 387.3.bn.a 12 12
387.3.bn.b 72
387.3.bn.c 84
387.3.bn.d 96
387.3.bn.e 168

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(387))\) into lower level spaces

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