Space of modular forms of level 539 and weight 2

• Label: 539.2
• Level: 539
• Weight: 2
• Dimension: 10662
• Nonzero newspaces: 16
• Newform subspaces: 70
• Sturm bound: 47040
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 70 \)
Sturm bound:			\(47040\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(539))\).

	Total	New	Old
Modular forms	12360	11534	826
Cusp forms	11161	10662	499
Eisenstein series	1199	872	327

Trace form

10662 * q - 119 * q^2 - 121 * q^3 - 127 * q^4 - 125 * q^5 - 142 * q^6 - 152 * q^7 - 237 * q^8 - 149 * q^9 - 164 * q^10 - 151 * q^11 - 344 * q^12 - 146 * q^13 - 180 * q^14 - 265 * q^15 - 205 * q^16 - 164 * q^17 - 221 * q^18 - 168 * q^19 - 232 * q^20 - 194 * q^21 - 302 * q^22 - 331 * q^23 - 288 * q^24 - 205 * q^25 - 242 * q^26 - 223 * q^27 - 236 * q^28 - 282 * q^29 - 322 * q^30 - 197 * q^31 - 289 * q^32 - 222 * q^33 - 416 * q^34 - 222 * q^35 - 361 * q^36 - 163 * q^37 - 204 * q^38 - 182 * q^39 - 126 * q^40 - 158 * q^41 - 138 * q^42 - 246 * q^43 - 162 * q^44 - 284 * q^45 - 70 * q^46 - 160 * q^47 - 126 * q^48 - 68 * q^49 - 463 * q^50 - 154 * q^51 - 86 * q^52 - 192 * q^53 - 226 * q^54 - 161 * q^55 - 276 * q^56 - 348 * q^57 - 210 * q^58 - 199 * q^59 - 2 * q^60 - 124 * q^61 - 206 * q^62 - 174 * q^63 - 197 * q^64 - 176 * q^65 + 77 * q^66 - 349 * q^67 - 130 * q^68 - 95 * q^69 - 210 * q^70 - 171 * q^71 + 27 * q^72 - 146 * q^73 - 216 * q^74 + 4 * q^75 + 132 * q^76 - 153 * q^77 - 262 * q^78 - 178 * q^79 + 56 * q^80 + 178 * q^81 - 20 * q^82 - 18 * q^83 + 292 * q^84 - 110 * q^85 + 162 * q^86 + 168 * q^87 + 117 * q^88 - 225 * q^89 + 472 * q^90 - 76 * q^91 - 164 * q^92 + 185 * q^93 - 58 * q^94 - 72 * q^95 + 406 * q^96 - 199 * q^97 + 156 * q^98 - 553 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)

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
539.2.a	\(\chi_{539}(1, \cdot)\)	539.2.a.a	1	1
		539.2.a.b	1
		539.2.a.c	1
		539.2.a.d	1
		539.2.a.e	2
		539.2.a.f	2
		539.2.a.g	3
		539.2.a.h	3
		539.2.a.i	3
		539.2.a.j	3
		539.2.a.k	4
		539.2.a.l	10
539.2.b	\(\chi_{539}(538, \cdot)\)	539.2.b.a	8	1
		539.2.b.b	12
		539.2.b.c	16
539.2.e	\(\chi_{539}(67, \cdot)\)	539.2.e.a	2	2
		539.2.e.b	2
		539.2.e.c	2
		539.2.e.d	2
		539.2.e.e	2
		539.2.e.f	2
		539.2.e.g	2
		539.2.e.h	2
		539.2.e.i	4
		539.2.e.j	4
		539.2.e.k	4
		539.2.e.l	6
		539.2.e.m	6
		539.2.e.n	8
		539.2.e.o	20
539.2.f	\(\chi_{539}(148, \cdot)\)	539.2.f.a	4	4
		539.2.f.b	4
		539.2.f.c	8
		539.2.f.d	8
		539.2.f.e	16
		539.2.f.f	16
		539.2.f.g	20
		539.2.f.h	20
		539.2.f.i	48
539.2.i	\(\chi_{539}(362, \cdot)\)	539.2.i.a	4	2
		539.2.i.b	8
		539.2.i.c	12
		539.2.i.d	16
		539.2.i.e	32
539.2.j	\(\chi_{539}(78, \cdot)\)	539.2.j.a	144	6
		539.2.j.b	144
539.2.m	\(\chi_{539}(195, \cdot)\)	539.2.m.a	48	4
		539.2.m.b	96
539.2.p	\(\chi_{539}(76, \cdot)\)	539.2.p.a	324	6
539.2.q	\(\chi_{539}(214, \cdot)\)	539.2.q.a	8	8
		539.2.q.b	16
		539.2.q.c	16
		539.2.q.d	16
		539.2.q.e	32
		539.2.q.f	32
		539.2.q.g	32
		539.2.q.h	40
		539.2.q.i	96
539.2.r	\(\chi_{539}(23, \cdot)\)	539.2.r.a	276	12
		539.2.r.b	276
539.2.s	\(\chi_{539}(19, \cdot)\)	539.2.s.a	16	8
		539.2.s.b	16
		539.2.s.c	16
		539.2.s.d	48
		539.2.s.e	192
539.2.v	\(\chi_{539}(15, \cdot)\)	539.2.v.a	1296	24
539.2.w	\(\chi_{539}(10, \cdot)\)	539.2.w.a	648	12
539.2.z	\(\chi_{539}(6, \cdot)\)	539.2.z.a	1296	24
539.2.bc	\(\chi_{539}(4, \cdot)\)	539.2.bc.a	2592	48
539.2.bf	\(\chi_{539}(17, \cdot)\)	539.2.bf.a	2592	48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(539))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(539)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)