Properties

Label 387.5
Level 387
Weight 5
Dimension 17351
Nonzero newspaces 20
Sturm bound 55440
Trace bound 5

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Defining parameters

Level: \( N \) = \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(55440\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(387))\).

Total New Old
Modular forms 22512 17721 4791
Cusp forms 21840 17351 4489
Eisenstein series 672 370 302

Trace form

\( 17351 q - 57 q^{2} - 78 q^{3} - 85 q^{4} - 39 q^{5} + 114 q^{6} + 25 q^{7} - 63 q^{8} - 282 q^{9} + O(q^{10}) \) \( 17351 q - 57 q^{2} - 78 q^{3} - 85 q^{4} - 39 q^{5} + 114 q^{6} + 25 q^{7} - 63 q^{8} - 282 q^{9} - 621 q^{10} - 1029 q^{11} - 744 q^{12} + 397 q^{13} + 2229 q^{14} + 1968 q^{15} + 1043 q^{16} - 63 q^{17} - 2892 q^{18} - 1913 q^{19} - 3291 q^{20} - 1044 q^{21} + 963 q^{22} + 501 q^{23} + 2814 q^{24} + 1511 q^{25} - 63 q^{26} - 192 q^{27} - 3029 q^{28} + 2049 q^{29} + 2472 q^{30} + 3356 q^{31} + 17379 q^{32} - 642 q^{33} - 4617 q^{34} - 6237 q^{35} + 4686 q^{36} - 7199 q^{37} - 18645 q^{38} - 4032 q^{39} - 30027 q^{40} - 17022 q^{41} - 19308 q^{42} + 5675 q^{43} + 13986 q^{44} + 8340 q^{45} + 50403 q^{46} + 26466 q^{47} + 13458 q^{48} + 26938 q^{49} + 18075 q^{50} - 4998 q^{51} + 4001 q^{52} - 6993 q^{53} + 726 q^{54} - 38451 q^{55} - 48531 q^{56} - 10818 q^{57} - 29763 q^{58} - 12513 q^{59} - 15024 q^{60} - 17795 q^{61} - 63 q^{62} + 15072 q^{63} - 17233 q^{64} + 14253 q^{65} + 27384 q^{66} + 25183 q^{67} + 20943 q^{68} + 27672 q^{69} + 140517 q^{70} + 31689 q^{71} - 16986 q^{72} + 1615 q^{73} - 96630 q^{74} - 42126 q^{75} - 81422 q^{76} - 95943 q^{77} + 24036 q^{78} - 53975 q^{79} - 113463 q^{80} - 36858 q^{81} - 109179 q^{82} - 23547 q^{83} + 12216 q^{84} - 14190 q^{85} + 66396 q^{86} + 42960 q^{87} + 58227 q^{88} + 54369 q^{89} - 41664 q^{90} - 8821 q^{91} + 131115 q^{92} - 38592 q^{93} + 164961 q^{94} + 102261 q^{95} + 7260 q^{96} + 156751 q^{97} + 51534 q^{98} + 18168 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(387))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
387.5.b \(\chi_{387}(343, \cdot)\) 387.5.b.a 1 1
387.5.b.b 2
387.5.b.c 12
387.5.b.d 28
387.5.b.e 30
387.5.c \(\chi_{387}(44, \cdot)\) 387.5.c.a 56 1
387.5.i \(\chi_{387}(251, \cdot)\) n/a 116 2
387.5.j \(\chi_{387}(37, \cdot)\) n/a 144 2
387.5.n \(\chi_{387}(265, \cdot)\) n/a 348 2
387.5.o \(\chi_{387}(92, \cdot)\) n/a 348 2
387.5.p \(\chi_{387}(221, \cdot)\) n/a 348 2
387.5.q \(\chi_{387}(173, \cdot)\) n/a 336 2
387.5.r \(\chi_{387}(7, \cdot)\) n/a 348 2
387.5.s \(\chi_{387}(85, \cdot)\) n/a 348 2
387.5.w \(\chi_{387}(82, \cdot)\) n/a 438 6
387.5.x \(\chi_{387}(35, \cdot)\) n/a 360 6
387.5.bd \(\chi_{387}(11, \cdot)\) n/a 2088 12
387.5.be \(\chi_{387}(23, \cdot)\) n/a 2088 12
387.5.bf \(\chi_{387}(22, \cdot)\) n/a 2088 12
387.5.bg \(\chi_{387}(34, \cdot)\) n/a 2088 12
387.5.bh \(\chi_{387}(106, \cdot)\) n/a 2088 12
387.5.bi \(\chi_{387}(14, \cdot)\) n/a 2088 12
387.5.bm \(\chi_{387}(17, \cdot)\) n/a 696 12
387.5.bn \(\chi_{387}(19, \cdot)\) n/a 864 12

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(387))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(387)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 2}\)