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Properties

Label 387.6
Level 387
Weight 6
Dimension 21738
Nonzero newspaces 20
Sturm bound 66528
Trace bound 5

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Defining parameters

Level: \( N \) = \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(66528\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(387))\).

Total New Old
Modular forms 28056 22106 5950
Cusp forms 27384 21738 5646
Eisenstein series 672 368 304

Trace form

\( 21738 q - 81 q^{2} - 60 q^{3} + 27 q^{4} - 207 q^{5} - 426 q^{6} - 39 q^{7} + 1773 q^{8} + 744 q^{9} + O(q^{10}) \) \( 21738 q - 81 q^{2} - 60 q^{3} + 27 q^{4} - 207 q^{5} - 426 q^{6} - 39 q^{7} + 1773 q^{8} + 744 q^{9} - 237 q^{10} - 2079 q^{11} - 5532 q^{12} - 975 q^{13} - 2367 q^{14} + 4020 q^{15} + 2787 q^{16} + 10413 q^{17} + 16116 q^{18} - 981 q^{19} - 13383 q^{20} - 17424 q^{21} - 8853 q^{22} - 19431 q^{23} - 1182 q^{24} + 9423 q^{25} + 42057 q^{26} + 20220 q^{27} + 3339 q^{28} - 14823 q^{29} - 44292 q^{30} - 41570 q^{31} - 74397 q^{32} + 17556 q^{33} + 70659 q^{34} + 95703 q^{35} + 29094 q^{36} + 67785 q^{37} + 39315 q^{38} - 16524 q^{39} - 175455 q^{40} - 49038 q^{41} - 20280 q^{42} - 184320 q^{43} - 223314 q^{44} - 86160 q^{45} - 115965 q^{46} - 22776 q^{47} + 114726 q^{48} + 129820 q^{49} + 403455 q^{50} + 18708 q^{51} + 384205 q^{52} + 100671 q^{53} - 16446 q^{54} - 76623 q^{55} - 253371 q^{56} + 208512 q^{57} + 38937 q^{58} - 40383 q^{59} - 176700 q^{60} - 175863 q^{61} - 536391 q^{62} - 267132 q^{63} - 13761 q^{64} + 33885 q^{65} + 201912 q^{66} + 60369 q^{67} + 253251 q^{68} + 251880 q^{69} - 696735 q^{70} + 63375 q^{71} - 70986 q^{72} + 66909 q^{73} + 1341012 q^{74} + 37380 q^{75} + 1004784 q^{76} + 565623 q^{77} - 362928 q^{78} + 158709 q^{79} - 434919 q^{80} - 389208 q^{81} - 579543 q^{82} - 566907 q^{83} - 215448 q^{84} - 675240 q^{85} - 1241364 q^{86} + 285744 q^{87} - 935709 q^{88} + 387201 q^{89} + 1079700 q^{90} - 150849 q^{91} + 283539 q^{92} - 227880 q^{93} + 687705 q^{94} + 199389 q^{95} - 85620 q^{96} + 1314735 q^{97} + 1760700 q^{98} - 67476 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(387))\)

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
387.6.a \(\chi_{387}(1, \cdot)\) 387.6.a.a 6 1
387.6.a.b 8
387.6.a.c 8
387.6.a.d 9
387.6.a.e 10
387.6.a.f 11
387.6.a.g 16
387.6.a.h 20
387.6.d \(\chi_{387}(386, \cdot)\) 387.6.d.a 4 1
387.6.d.b 68
387.6.e \(\chi_{387}(49, \cdot)\) n/a 436 2
387.6.f \(\chi_{387}(130, \cdot)\) n/a 420 2
387.6.g \(\chi_{387}(178, \cdot)\) n/a 436 2
387.6.h \(\chi_{387}(208, \cdot)\) n/a 182 2
387.6.k \(\chi_{387}(308, \cdot)\) n/a 436 2
387.6.l \(\chi_{387}(128, \cdot)\) n/a 436 2
387.6.m \(\chi_{387}(50, \cdot)\) n/a 436 2
387.6.t \(\chi_{387}(80, \cdot)\) n/a 148 2
387.6.u \(\chi_{387}(64, \cdot)\) n/a 540 6
387.6.v \(\chi_{387}(8, \cdot)\) n/a 432 6
387.6.y \(\chi_{387}(10, \cdot)\) n/a 1092 12
387.6.z \(\chi_{387}(13, \cdot)\) n/a 2616 12
387.6.ba \(\chi_{387}(4, \cdot)\) n/a 2616 12
387.6.bb \(\chi_{387}(25, \cdot)\) n/a 2616 12
387.6.bc \(\chi_{387}(26, \cdot)\) n/a 888 12
387.6.bj \(\chi_{387}(20, \cdot)\) n/a 2616 12
387.6.bk \(\chi_{387}(2, \cdot)\) n/a 2616 12
387.6.bl \(\chi_{387}(5, \cdot)\) n/a 2616 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(387))\) into lower level spaces

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