Space of modular forms of level 555 and weight 2

• Label: 555.2
• Level: 555
• Weight: 2
• Dimension: 7307
• Nonzero newspaces: 30
• Newform subspaces: 56
• Sturm bound: 43776
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Newform subspaces:			\( 56 \)
Sturm bound:			\(43776\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(555))\).

	Total	New	Old
Modular forms	11520	7723	3797
Cusp forms	10369	7307	3062
Eisenstein series	1151	416	735

Trace form

7307 * q + 5 * q^2 - 33 * q^3 - 63 * q^4 - q^5 - 107 * q^6 - 64 * q^7 + 9 * q^8 - 37 * q^9 - 103 * q^10 + 20 * q^11 - 31 * q^12 - 54 * q^13 + 24 * q^14 - 51 * q^15 - 183 * q^16 + 14 * q^17 - 31 * q^18 - 60 * q^19 + 9 * q^20 - 100 * q^21 - 44 * q^22 + 24 * q^23 - 15 * q^24 - 109 * q^25 + 2 * q^26 - 45 * q^27 - 256 * q^28 - 38 * q^29 - 125 * q^30 - 400 * q^31 - 215 * q^32 - 104 * q^33 - 302 * q^34 - 100 * q^35 - 243 * q^36 - 193 * q^37 - 76 * q^38 - 110 * q^39 - 369 * q^40 - 194 * q^41 - 156 * q^42 - 180 * q^43 - 212 * q^44 - 55 * q^45 - 432 * q^46 - 40 * q^47 - 127 * q^48 - 97 * q^49 - 13 * q^50 - 86 * q^51 + 22 * q^52 + 74 * q^53 - 35 * q^54 - 88 * q^55 + 120 * q^56 - 8 * q^57 - 58 * q^58 - 76 * q^59 - 175 * q^60 - 330 * q^61 - 264 * q^62 - 244 * q^63 - 463 * q^64 - 144 * q^65 - 568 * q^66 - 172 * q^67 - 302 * q^68 - 300 * q^69 - 480 * q^70 - 200 * q^71 - 459 * q^72 - 378 * q^73 - 475 * q^74 - 285 * q^75 - 788 * q^76 - 192 * q^77 - 494 * q^78 - 280 * q^79 - 363 * q^80 - 397 * q^81 - 358 * q^82 - 84 * q^83 - 484 * q^84 - 256 * q^85 - 364 * q^86 - 226 * q^87 - 228 * q^88 - 78 * q^89 - 175 * q^90 - 248 * q^91 + 96 * q^92 + 104 * q^93 + 88 * q^94 + 12 * q^95 + 305 * q^96 + 22 * q^97 + 157 * q^98 + 164 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(555))\)

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
555.2.a	\(\chi_{555}(1, \cdot)\)	555.2.a.a	1	1
		555.2.a.b	1
		555.2.a.c	2
		555.2.a.d	2
		555.2.a.e	2
		555.2.a.f	2
		555.2.a.g	2
		555.2.a.h	3
		555.2.a.i	3
		555.2.a.j	5
555.2.c	\(\chi_{555}(334, \cdot)\)	555.2.c.a	2	1
		555.2.c.b	8
		555.2.c.c	26
555.2.e	\(\chi_{555}(406, \cdot)\)	555.2.e.a	2	1
		555.2.e.b	10
		555.2.e.c	12
555.2.g	\(\chi_{555}(184, \cdot)\)	555.2.g.a	40	1
555.2.i	\(\chi_{555}(121, \cdot)\)	555.2.i.a	2	2
		555.2.i.b	4
		555.2.i.c	4
		555.2.i.d	10
		555.2.i.e	14
		555.2.i.f	14
555.2.j	\(\chi_{555}(43, \cdot)\)	555.2.j.a	76	2
555.2.m	\(\chi_{555}(179, \cdot)\)	555.2.m.a	16	2
		555.2.m.b	128
555.2.n	\(\chi_{555}(332, \cdot)\)	555.2.n.a	32	2
		555.2.n.b	112
555.2.o	\(\chi_{555}(38, \cdot)\)	555.2.o.a	144	2
555.2.s	\(\chi_{555}(191, \cdot)\)	555.2.s.a	104	2
555.2.t	\(\chi_{555}(253, \cdot)\)	555.2.t.a	76	2
555.2.x	\(\chi_{555}(64, \cdot)\)	555.2.x.a	80	2
555.2.z	\(\chi_{555}(196, \cdot)\)	555.2.z.a	20	2
		555.2.z.b	28
555.2.bb	\(\chi_{555}(454, \cdot)\)	555.2.bb.a	72	2
555.2.bc	\(\chi_{555}(16, \cdot)\)	555.2.bc.a	6	6
		555.2.bc.b	36
		555.2.bc.c	36
		555.2.bc.d	36
		555.2.bc.e	42
555.2.bd	\(\chi_{555}(82, \cdot)\)	555.2.bd.a	152	4
555.2.bg	\(\chi_{555}(236, \cdot)\)	555.2.bg.a	208	4
555.2.bh	\(\chi_{555}(122, \cdot)\)	555.2.bh.a	288	4
555.2.bi	\(\chi_{555}(47, \cdot)\)	555.2.bi.a	288	4
555.2.bm	\(\chi_{555}(14, \cdot)\)	555.2.bm.a	288	4
555.2.bn	\(\chi_{555}(193, \cdot)\)	555.2.bn.a	152	4
555.2.bp	\(\chi_{555}(4, \cdot)\)	555.2.bp.a	240	6
555.2.bs	\(\chi_{555}(34, \cdot)\)	555.2.bs.a	216	6
555.2.bt	\(\chi_{555}(136, \cdot)\)	555.2.bt.a	72	6
		555.2.bt.b	84
555.2.bx	\(\chi_{555}(22, \cdot)\)	555.2.bx.a	456	12
555.2.bz	\(\chi_{555}(56, \cdot)\)	555.2.bz.a	600	12
555.2.ca	\(\chi_{555}(59, \cdot)\)	555.2.ca.a	864	12
555.2.cc	\(\chi_{555}(53, \cdot)\)	555.2.cc.a	864	12
555.2.cf	\(\chi_{555}(62, \cdot)\)	555.2.cf.a	864	12
555.2.ch	\(\chi_{555}(13, \cdot)\)	555.2.ch.a	456	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(555))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(555)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 2}\)