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Properties

Label 387.4
Level 387
Weight 4
Dimension 12968
Nonzero newspaces 20
Sturm bound 44352
Trace bound 5

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Defining parameters

Level: \( N \) = \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(44352\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(387))\).

Total New Old
Modular forms 16968 13336 3632
Cusp forms 16296 12968 3328
Eisenstein series 672 368 304

Trace form

\( 12968 q - 57 q^{2} - 78 q^{3} - 37 q^{4} - 33 q^{5} - 102 q^{6} - 89 q^{7} - 195 q^{8} - 174 q^{9} + O(q^{10}) \) \( 12968 q - 57 q^{2} - 78 q^{3} - 37 q^{4} - 33 q^{5} - 102 q^{6} - 89 q^{7} - 195 q^{8} - 174 q^{9} - 213 q^{10} + 69 q^{11} + 228 q^{12} + 55 q^{13} + 57 q^{14} - 138 q^{15} - 205 q^{16} - 459 q^{17} - 516 q^{18} + 7 q^{19} - 87 q^{20} - 126 q^{21} - 129 q^{22} + 3 q^{23} + 114 q^{24} - 55 q^{25} + 993 q^{26} + 780 q^{27} - 533 q^{28} - 165 q^{29} - 660 q^{30} - 1223 q^{31} - 3765 q^{32} - 480 q^{33} - 1359 q^{34} - 663 q^{35} + 366 q^{36} + 295 q^{37} + 663 q^{38} - 1602 q^{39} + 6513 q^{40} + 1041 q^{41} + 888 q^{42} + 4955 q^{43} + 4158 q^{44} + 1266 q^{45} + 3387 q^{46} + 1197 q^{47} - 42 q^{48} - 1203 q^{49} - 2097 q^{50} - 678 q^{51} - 8099 q^{52} - 3135 q^{53} - 2514 q^{54} - 7485 q^{55} - 5811 q^{56} + 2358 q^{57} - 183 q^{58} + 1533 q^{59} - 12 q^{60} + 451 q^{61} - 519 q^{62} - 1290 q^{63} + 3743 q^{64} + 267 q^{65} + 1896 q^{66} + 3673 q^{67} + 1323 q^{68} - 1866 q^{69} - 12447 q^{70} - 10785 q^{71} - 1866 q^{72} - 3731 q^{73} - 5340 q^{74} + 642 q^{75} - 2960 q^{76} + 1245 q^{77} + 1896 q^{78} + 175 q^{79} + 8793 q^{80} + 1050 q^{81} + 7881 q^{82} + 8199 q^{83} - 1032 q^{84} + 8244 q^{85} + 14250 q^{86} + 138 q^{87} + 15483 q^{88} + 7653 q^{89} + 1428 q^{90} + 10355 q^{91} + 7251 q^{92} + 342 q^{93} + 6321 q^{94} - 747 q^{95} - 2244 q^{96} - 1853 q^{97} - 8808 q^{98} - 678 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(387))\)

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
387.4.a \(\chi_{387}(1, \cdot)\) 387.4.a.a 1 1
387.4.a.b 1
387.4.a.c 2
387.4.a.d 2
387.4.a.e 4
387.4.a.f 5
387.4.a.g 5
387.4.a.h 6
387.4.a.i 8
387.4.a.j 8
387.4.a.k 10
387.4.d \(\chi_{387}(386, \cdot)\) 387.4.d.a 4 1
387.4.d.b 4
387.4.d.c 36
387.4.e \(\chi_{387}(49, \cdot)\) n/a 260 2
387.4.f \(\chi_{387}(130, \cdot)\) n/a 252 2
387.4.g \(\chi_{387}(178, \cdot)\) n/a 260 2
387.4.h \(\chi_{387}(208, \cdot)\) n/a 108 2
387.4.k \(\chi_{387}(308, \cdot)\) n/a 260 2
387.4.l \(\chi_{387}(128, \cdot)\) n/a 260 2
387.4.m \(\chi_{387}(50, \cdot)\) n/a 260 2
387.4.t \(\chi_{387}(80, \cdot)\) 387.4.t.a 88 2
387.4.u \(\chi_{387}(64, \cdot)\) n/a 324 6
387.4.v \(\chi_{387}(8, \cdot)\) n/a 264 6
387.4.y \(\chi_{387}(10, \cdot)\) n/a 648 12
387.4.z \(\chi_{387}(13, \cdot)\) n/a 1560 12
387.4.ba \(\chi_{387}(4, \cdot)\) n/a 1560 12
387.4.bb \(\chi_{387}(25, \cdot)\) n/a 1560 12
387.4.bc \(\chi_{387}(26, \cdot)\) n/a 528 12
387.4.bj \(\chi_{387}(20, \cdot)\) n/a 1560 12
387.4.bk \(\chi_{387}(2, \cdot)\) n/a 1560 12
387.4.bl \(\chi_{387}(5, \cdot)\) n/a 1560 12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(387))\) into lower level spaces

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