Space of modular forms of level 287 and weight 4

• Label: 287.4
• Level: 287
• Weight: 4
• Dimension: 9454
• Nonzero newspaces: 16
• Sturm bound: 26880
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(26880\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(287))\).

	Total	New	Old
Modular forms	10320	9846	474
Cusp forms	9840	9454	386
Eisenstein series	480	392	88

Trace form

9454 * q - 74 * q^2 - 62 * q^3 - 74 * q^4 - 98 * q^5 - 140 * q^6 - 142 * q^7 - 134 * q^8 + 10 * q^9 - 20 * q^10 - 74 * q^11 - 164 * q^12 - 80 * q^13 - 142 * q^14 - 332 * q^15 - 194 * q^16 - 230 * q^17 - 38 * q^18 + 238 * q^19 + 256 * q^20 + 362 * q^21 - 176 * q^22 - 494 * q^23 - 356 * q^24 - 494 * q^25 - 80 * q^26 - 140 * q^27 - 478 * q^28 - 212 * q^29 + 5652 * q^30 + 2190 * q^31 + 5042 * q^32 + 1738 * q^33 + 396 * q^34 - 374 * q^35 - 5770 * q^36 - 2510 * q^37 - 2824 * q^38 - 6244 * q^39 - 10456 * q^40 - 2562 * q^41 - 7036 * q^42 - 1320 * q^43 - 6872 * q^44 - 2236 * q^45 - 1420 * q^46 + 562 * q^47 + 5012 * q^48 + 886 * q^49 + 5670 * q^50 + 8242 * q^51 + 13304 * q^52 + 5490 * q^53 + 11340 * q^54 + 316 * q^55 + 1454 * q^56 - 2012 * q^57 - 68 * q^58 - 1910 * q^59 - 920 * q^60 + 70 * q^61 - 1232 * q^62 - 730 * q^63 - 1658 * q^64 + 2648 * q^65 + 25252 * q^66 + 15742 * q^67 + 21044 * q^68 + 16564 * q^69 + 10856 * q^70 + 7704 * q^71 + 2794 * q^72 - 2342 * q^73 - 5696 * q^74 - 13100 * q^75 - 31436 * q^76 - 5442 * q^77 - 27128 * q^78 - 13166 * q^79 - 32896 * q^80 - 30100 * q^81 - 38078 * q^82 - 14564 * q^83 - 17352 * q^84 - 24800 * q^85 - 24720 * q^86 - 7868 * q^87 - 15200 * q^88 - 6198 * q^89 - 7448 * q^90 + 2516 * q^91 + 4888 * q^92 + 10186 * q^93 + 29668 * q^94 + 20286 * q^95 + 53116 * q^96 + 28300 * q^97 + 16942 * q^98 + 26872 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(287))\)

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
287.4.a	\(\chi_{287}(1, \cdot)\)	287.4.a.a	1	1
		287.4.a.b	11
		287.4.a.c	12
		287.4.a.d	17
		287.4.a.e	19
287.4.c	\(\chi_{287}(204, \cdot)\)	287.4.c.a	62	1
287.4.e	\(\chi_{287}(165, \cdot)\)	287.4.e.a	72	2
		287.4.e.b	88
287.4.f	\(\chi_{287}(50, \cdot)\)	n/a	128	2
287.4.h	\(\chi_{287}(57, \cdot)\)	n/a	248	4
287.4.j	\(\chi_{287}(81, \cdot)\)	n/a	164	2
287.4.l	\(\chi_{287}(27, \cdot)\)	n/a	328	4
287.4.n	\(\chi_{287}(64, \cdot)\)	n/a	248	4
287.4.r	\(\chi_{287}(9, \cdot)\)	n/a	328	4
287.4.s	\(\chi_{287}(16, \cdot)\)	n/a	656	8
287.4.u	\(\chi_{287}(8, \cdot)\)	n/a	512	8
287.4.w	\(\chi_{287}(3, \cdot)\)	n/a	656	8
287.4.z	\(\chi_{287}(4, \cdot)\)	n/a	656	8
287.4.bb	\(\chi_{287}(6, \cdot)\)	n/a	1312	16
287.4.bc	\(\chi_{287}(2, \cdot)\)	n/a	1312	16
287.4.be	\(\chi_{287}(12, \cdot)\)	n/a	2624	32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(287))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(287)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 2}\)