Space of modular forms of level 583 and weight 2

• Label: 583.2
• Level: 583
• Weight: 2
• Dimension: 13335
• Nonzero newspaces: 12
• Newform subspaces: 32
• Sturm bound: 56160
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 583 = 11 \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 32 \)
Sturm bound:			\(56160\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(583))\).

	Total	New	Old
Modular forms	14560	14255	305
Cusp forms	13521	13335	186
Eisenstein series	1039	920	119

Trace form

13335 * q - 207 * q^2 - 210 * q^3 - 219 * q^4 - 216 * q^5 - 224 * q^6 - 212 * q^7 - 223 * q^8 - 217 * q^9 - 222 * q^10 - 237 * q^11 - 492 * q^12 - 230 * q^13 - 240 * q^14 - 230 * q^15 - 231 * q^16 - 222 * q^17 - 255 * q^18 - 228 * q^19 - 254 * q^20 - 244 * q^21 - 233 * q^22 - 490 * q^23 - 268 * q^24 - 231 * q^25 - 234 * q^26 - 258 * q^27 - 256 * q^28 - 238 * q^29 - 284 * q^30 - 254 * q^31 - 287 * q^32 - 236 * q^33 - 530 * q^34 - 252 * q^35 - 291 * q^36 - 252 * q^37 - 268 * q^38 - 256 * q^39 - 220 * q^40 - 182 * q^41 - 88 * q^42 - 136 * q^43 - 141 * q^44 - 282 * q^45 - 180 * q^46 - 220 * q^47 + 180 * q^48 - 155 * q^49 - 83 * q^50 - 76 * q^51 + 42 * q^52 - 99 * q^53 - 204 * q^54 - 164 * q^55 - 276 * q^56 - 80 * q^57 - 64 * q^58 - 174 * q^59 + 148 * q^60 - 242 * q^61 - 172 * q^62 - 60 * q^63 - 111 * q^64 - 196 * q^65 - 146 * q^66 - 470 * q^67 - 248 * q^68 - 306 * q^69 - 360 * q^70 - 274 * q^71 - 403 * q^72 - 290 * q^73 - 310 * q^74 - 340 * q^75 - 348 * q^76 - 238 * q^77 - 652 * q^78 - 268 * q^79 - 386 * q^80 - 331 * q^81 - 366 * q^82 - 280 * q^83 - 440 * q^84 - 312 * q^85 - 364 * q^86 - 224 * q^87 - 119 * q^88 - 458 * q^89 - 34 * q^90 - 96 * q^91 + 96 * q^92 - 114 * q^93 + 304 * q^94 - 120 * q^95 + 76 * q^96 + 150 * q^97 + 25 * q^98 + 17 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(583))\)

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
583.2.a	\(\chi_{583}(1, \cdot)\)	583.2.a.a	1	1
		583.2.a.b	1
		583.2.a.c	1
		583.2.a.d	2
		583.2.a.e	2
		583.2.a.f	6
		583.2.a.g	8
		583.2.a.h	10
		583.2.a.i	12
583.2.b	\(\chi_{583}(529, \cdot)\)	583.2.b.a	2	1
		583.2.b.b	2
		583.2.b.c	2
		583.2.b.d	6
		583.2.b.e	8
		583.2.b.f	24
583.2.f	\(\chi_{583}(76, \cdot)\)	583.2.f.a	4	2
		583.2.f.b	100
583.2.g	\(\chi_{583}(213, \cdot)\)	583.2.g.a	4	4
		583.2.g.b	4
		583.2.g.c	96
		583.2.g.d	104
583.2.j	\(\chi_{583}(158, \cdot)\)	583.2.j.a	208	4
583.2.k	\(\chi_{583}(89, \cdot)\)	583.2.k.a	252	12
		583.2.k.b	300
583.2.l	\(\chi_{583}(30, \cdot)\)	583.2.l.a	416	8
583.2.p	\(\chi_{583}(78, \cdot)\)	583.2.p.a	240	12
		583.2.p.b	288
583.2.q	\(\chi_{583}(21, \cdot)\)	583.2.q.a	48	24
		583.2.q.b	1200
583.2.s	\(\chi_{583}(15, \cdot)\)	583.2.s.a	2496	48
583.2.t	\(\chi_{583}(4, \cdot)\)	583.2.t.a	2496	48
583.2.x	\(\chi_{583}(2, \cdot)\)	583.2.x.a	4992	96

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(583))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(583)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 2}\)