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Properties

Label 1386.4
Level 1386
Weight 4
Dimension 38674
Nonzero newspaces 40
Sturm bound 414720
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(414720\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1386))\).

Total New Old
Modular forms 157440 38674 118766
Cusp forms 153600 38674 114926
Eisenstein series 3840 0 3840

Trace form

\( 38674 q + 16 q^{2} + 12 q^{3} - 32 q^{4} + 96 q^{5} - 72 q^{6} + 68 q^{7} - 32 q^{8} - 420 q^{9} + O(q^{10}) \) \( 38674 q + 16 q^{2} + 12 q^{3} - 32 q^{4} + 96 q^{5} - 72 q^{6} + 68 q^{7} - 32 q^{8} - 420 q^{9} + 80 q^{10} + 212 q^{11} + 96 q^{12} + 580 q^{13} + 908 q^{14} + 840 q^{15} - 128 q^{16} - 1280 q^{17} - 48 q^{18} - 526 q^{19} - 528 q^{20} - 1512 q^{21} - 732 q^{22} + 704 q^{23} + 512 q^{24} + 1588 q^{25} + 200 q^{26} + 1344 q^{27} - 344 q^{28} - 1972 q^{29} - 2592 q^{30} - 1024 q^{31} - 704 q^{32} - 4126 q^{33} - 1416 q^{34} - 350 q^{35} + 1664 q^{36} - 1756 q^{37} + 872 q^{38} - 3648 q^{39} + 960 q^{40} + 656 q^{41} + 688 q^{42} + 4696 q^{43} + 992 q^{44} - 632 q^{45} + 288 q^{46} - 3304 q^{47} - 576 q^{48} + 7778 q^{49} - 1456 q^{50} - 4264 q^{51} + 3440 q^{52} + 18132 q^{53} + 2376 q^{54} + 7040 q^{55} + 448 q^{56} + 11212 q^{57} + 96 q^{58} + 5070 q^{59} + 4320 q^{60} - 9320 q^{61} + 3632 q^{62} + 12524 q^{63} + 1024 q^{64} + 1944 q^{65} + 5376 q^{66} - 10824 q^{67} + 3424 q^{68} + 5344 q^{69} - 5352 q^{70} - 12544 q^{71} - 96 q^{72} - 5152 q^{73} - 8208 q^{74} - 6928 q^{75} - 2528 q^{76} - 12212 q^{77} - 16560 q^{78} - 3124 q^{79} - 4480 q^{80} - 19868 q^{81} + 1948 q^{82} - 32934 q^{83} - 7472 q^{84} - 3208 q^{85} - 1516 q^{86} - 16984 q^{87} + 4592 q^{88} + 20400 q^{89} + 18848 q^{90} + 24150 q^{91} + 9024 q^{92} + 21704 q^{93} + 10520 q^{94} + 45132 q^{95} + 768 q^{96} - 3730 q^{97} - 3404 q^{98} + 61688 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1386))\)

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
1386.4.a \(\chi_{1386}(1, \cdot)\) 1386.4.a.a 1 1
1386.4.a.b 1
1386.4.a.c 1
1386.4.a.d 1
1386.4.a.e 1
1386.4.a.f 1
1386.4.a.g 1
1386.4.a.h 1
1386.4.a.i 1
1386.4.a.j 1
1386.4.a.k 1
1386.4.a.l 1
1386.4.a.m 1
1386.4.a.n 1
1386.4.a.o 2
1386.4.a.p 2
1386.4.a.q 2
1386.4.a.r 2
1386.4.a.s 2
1386.4.a.t 2
1386.4.a.u 2
1386.4.a.v 2
1386.4.a.w 2
1386.4.a.x 2
1386.4.a.y 2
1386.4.a.z 2
1386.4.a.ba 2
1386.4.a.bb 2
1386.4.a.bc 3
1386.4.a.bd 3
1386.4.a.be 3
1386.4.a.bf 3
1386.4.a.bg 3
1386.4.a.bh 3
1386.4.a.bi 3
1386.4.a.bj 3
1386.4.a.bk 4
1386.4.a.bl 4
1386.4.c \(\chi_{1386}(197, \cdot)\) 1386.4.c.a 36 1
1386.4.c.b 36
1386.4.e \(\chi_{1386}(307, \cdot)\) n/a 120 1
1386.4.g \(\chi_{1386}(881, \cdot)\) 1386.4.g.a 40 1
1386.4.g.b 40
1386.4.i \(\chi_{1386}(529, \cdot)\) n/a 480 2
1386.4.j \(\chi_{1386}(463, \cdot)\) n/a 360 2
1386.4.k \(\chi_{1386}(793, \cdot)\) n/a 200 2
1386.4.l \(\chi_{1386}(67, \cdot)\) n/a 480 2
1386.4.m \(\chi_{1386}(379, \cdot)\) n/a 360 4
1386.4.n \(\chi_{1386}(439, \cdot)\) n/a 576 2
1386.4.p \(\chi_{1386}(65, \cdot)\) n/a 576 2
1386.4.r \(\chi_{1386}(89, \cdot)\) n/a 160 2
1386.4.w \(\chi_{1386}(353, \cdot)\) n/a 480 2
1386.4.y \(\chi_{1386}(419, \cdot)\) n/a 480 2
1386.4.ba \(\chi_{1386}(989, \cdot)\) n/a 192 2
1386.4.bd \(\chi_{1386}(241, \cdot)\) n/a 576 2
1386.4.bf \(\chi_{1386}(769, \cdot)\) n/a 576 2
1386.4.bh \(\chi_{1386}(263, \cdot)\) n/a 576 2
1386.4.bj \(\chi_{1386}(659, \cdot)\) n/a 432 2
1386.4.bk \(\chi_{1386}(703, \cdot)\) n/a 240 2
1386.4.bn \(\chi_{1386}(551, \cdot)\) n/a 480 2
1386.4.bq \(\chi_{1386}(125, \cdot)\) n/a 384 4
1386.4.bs \(\chi_{1386}(811, \cdot)\) n/a 480 4
1386.4.bu \(\chi_{1386}(701, \cdot)\) n/a 288 4
1386.4.bw \(\chi_{1386}(445, \cdot)\) n/a 2304 8
1386.4.bx \(\chi_{1386}(37, \cdot)\) n/a 960 8
1386.4.by \(\chi_{1386}(169, \cdot)\) n/a 1728 8
1386.4.bz \(\chi_{1386}(25, \cdot)\) n/a 2304 8
1386.4.cb \(\chi_{1386}(47, \cdot)\) n/a 2304 8
1386.4.ce \(\chi_{1386}(19, \cdot)\) n/a 960 8
1386.4.cf \(\chi_{1386}(29, \cdot)\) n/a 1728 8
1386.4.ch \(\chi_{1386}(149, \cdot)\) n/a 2304 8
1386.4.cj \(\chi_{1386}(13, \cdot)\) n/a 2304 8
1386.4.cl \(\chi_{1386}(481, \cdot)\) n/a 2304 8
1386.4.co \(\chi_{1386}(107, \cdot)\) n/a 768 8
1386.4.cq \(\chi_{1386}(335, \cdot)\) n/a 2304 8
1386.4.cs \(\chi_{1386}(5, \cdot)\) n/a 2304 8
1386.4.cx \(\chi_{1386}(269, \cdot)\) n/a 768 8
1386.4.cz \(\chi_{1386}(95, \cdot)\) n/a 2304 8
1386.4.db \(\chi_{1386}(61, \cdot)\) n/a 2304 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1386))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1386)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(693))\)\(^{\oplus 2}\)