Space of modular forms of level 1587 and weight 4

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

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 - 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

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

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