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Properties

Label 1587.4
Level 1587
Weight 4
Dimension 207988
Nonzero newspaces 8
Sturm bound 744832
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1587 = 3 \cdot 23^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(744832\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1587))\).

Total New Old
Modular forms 280808 209396 71412
Cusp forms 277816 207988 69828
Eisenstein series 2992 1408 1584

Trace form

\( 207988 q - 231 q^{3} - 462 q^{4} - 231 q^{6} - 462 q^{7} - 231 q^{9} + O(q^{10}) \) \( 207988 q - 231 q^{3} - 462 q^{4} - 231 q^{6} - 462 q^{7} - 231 q^{9} - 462 q^{10} - 231 q^{12} - 462 q^{13} - 979 q^{15} - 2222 q^{16} - 352 q^{17} - 55 q^{18} - 22 q^{19} + 2816 q^{20} + 1089 q^{21} + 1430 q^{22} + 968 q^{23} + 2189 q^{24} + 946 q^{25} + 880 q^{26} - 99 q^{27} - 1870 q^{28} - 880 q^{29} - 3223 q^{30} - 2662 q^{31} - 5984 q^{32} - 2167 q^{33} - 8118 q^{34} - 5720 q^{35} - 2211 q^{36} - 5214 q^{37} - 2420 q^{38} + 33 q^{39} + 4818 q^{40} + 2200 q^{41} + 7029 q^{42} + 6402 q^{43} + 13244 q^{44} - 253 q^{45} + 7436 q^{46} + 7568 q^{47} + 6457 q^{48} + 8250 q^{49} + 7700 q^{50} + 1089 q^{51} + 858 q^{52} - 968 q^{53} + 4829 q^{54} - 8382 q^{55} - 14300 q^{56} - 3663 q^{57} - 24882 q^{58} - 12056 q^{59} - 6611 q^{60} - 462 q^{61} - 4411 q^{63} - 462 q^{64} - 11737 q^{66} - 462 q^{67} - 3982 q^{69} - 902 q^{70} - 15015 q^{72} - 462 q^{73} - 9460 q^{74} - 20163 q^{75} - 33242 q^{76} - 20944 q^{77} - 17347 q^{78} - 11902 q^{79} - 16236 q^{80} + 2497 q^{81} - 198 q^{82} + 3344 q^{83} + 33253 q^{84} + 21098 q^{85} + 26840 q^{86} + 18513 q^{87} + 24530 q^{88} + 22440 q^{89} + 37147 q^{90} + 31526 q^{91} + 18018 q^{92} + 23045 q^{93} + 32846 q^{94} + 16104 q^{95} + 10791 q^{96} - 9702 q^{97} - 10560 q^{98} + 3465 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1587))\)

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
1587.4.a \(\chi_{1587}(1, \cdot)\) 1587.4.a.a 2 1
1587.4.a.b 2
1587.4.a.c 2
1587.4.a.d 2
1587.4.a.e 4
1587.4.a.f 4
1587.4.a.g 4
1587.4.a.h 5
1587.4.a.i 5
1587.4.a.j 6
1587.4.a.k 6
1587.4.a.l 6
1587.4.a.m 6
1587.4.a.n 7
1587.4.a.o 7
1587.4.a.p 10
1587.4.a.q 14
1587.4.a.r 16
1587.4.a.s 24
1587.4.a.t 30
1587.4.a.u 30
1587.4.a.v 30
1587.4.a.w 30
1587.4.c \(\chi_{1587}(1586, \cdot)\) n/a 484 1
1587.4.e \(\chi_{1587}(118, \cdot)\) n/a 2520 10
1587.4.g \(\chi_{1587}(263, \cdot)\) n/a 4840 10
1587.4.i \(\chi_{1587}(70, \cdot)\) n/a 6072 22
1587.4.k \(\chi_{1587}(68, \cdot)\) n/a 12100 22
1587.4.m \(\chi_{1587}(4, \cdot)\) n/a 60720 220
1587.4.o \(\chi_{1587}(5, \cdot)\) n/a 121000 220

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1587))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1587)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1587))\)\(^{\oplus 1}\)