Space of modular forms of level 580 and weight 2

• Label: 580.2
• Level: 580
• Weight: 2
• Dimension: 5216
• Nonzero newspaces: 20
• Newform subspaces: 50
• Sturm bound: 40320
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 50 \)
Sturm bound:			\(40320\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(580))\).

	Total	New	Old
Modular forms	10640	5536	5104
Cusp forms	9521	5216	4305
Eisenstein series	1119	320	799

Trace form

5216 * q - 24 * q^2 + 4 * q^3 - 28 * q^4 - 74 * q^5 - 84 * q^6 - 4 * q^7 - 36 * q^8 - 58 * q^9 - 54 * q^10 - 28 * q^12 - 56 * q^13 - 28 * q^14 - 4 * q^15 - 68 * q^16 - 56 * q^17 - 16 * q^18 + 8 * q^19 - 34 * q^20 - 104 * q^21 - 28 * q^22 + 16 * q^23 - 28 * q^24 - 70 * q^25 - 92 * q^26 + 76 * q^27 - 56 * q^28 - 6 * q^29 - 84 * q^30 + 64 * q^31 - 44 * q^32 + 28 * q^33 - 28 * q^34 + 32 * q^35 - 108 * q^36 - 4 * q^37 - 28 * q^38 + 64 * q^39 - 34 * q^40 - 148 * q^41 - 28 * q^42 + 20 * q^43 - 56 * q^44 - 129 * q^45 - 224 * q^46 - 44 * q^47 - 252 * q^48 - 162 * q^49 - 112 * q^50 - 136 * q^51 - 244 * q^52 - 206 * q^53 - 280 * q^54 - 112 * q^55 - 280 * q^56 - 240 * q^57 - 372 * q^58 - 80 * q^59 - 210 * q^60 - 332 * q^61 - 224 * q^62 - 228 * q^63 - 280 * q^64 - 147 * q^65 - 308 * q^66 - 116 * q^67 - 200 * q^68 - 144 * q^69 - 154 * q^70 + 52 * q^71 - 144 * q^72 - 30 * q^73 - 56 * q^74 + 74 * q^75 - 84 * q^76 + 84 * q^77 - 28 * q^78 + 40 * q^79 - 74 * q^80 + 114 * q^81 - 60 * q^82 + 100 * q^83 + 56 * q^84 + 24 * q^85 - 112 * q^86 + 152 * q^87 - 56 * q^88 + 96 * q^89 - 96 * q^90 + 160 * q^91 - 28 * q^92 + 40 * q^93 - 28 * q^94 + 104 * q^95 - 210 * q^97 + 84 * q^98 + 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(580))\)

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
580.2.a	\(\chi_{580}(1, \cdot)\)	580.2.a.a	1	1
		580.2.a.b	1
		580.2.a.c	3
		580.2.a.d	3
580.2.c	\(\chi_{580}(349, \cdot)\)	580.2.c.a	4	1
		580.2.c.b	10
580.2.d	\(\chi_{580}(521, \cdot)\)	580.2.d.a	2	1
		580.2.d.b	4
		580.2.d.c	4
580.2.f	\(\chi_{580}(289, \cdot)\)	580.2.f.a	16	1
580.2.j	\(\chi_{580}(17, \cdot)\)	580.2.j.a	30	2
580.2.k	\(\chi_{580}(191, \cdot)\)	580.2.k.a	60	2
		580.2.k.b	60
580.2.n	\(\chi_{580}(407, \cdot)\)	580.2.n.a	2	2
		580.2.n.b	2
		580.2.n.c	8
		580.2.n.d	76
		580.2.n.e	80
580.2.o	\(\chi_{580}(347, \cdot)\)	580.2.o.a	2	2
		580.2.o.b	2
		580.2.o.c	12
		580.2.o.d	12
		580.2.o.e	144
580.2.r	\(\chi_{580}(99, \cdot)\)	580.2.r.a	2	2
		580.2.r.b	2
		580.2.r.c	4
		580.2.r.d	4
		580.2.r.e	160
580.2.s	\(\chi_{580}(133, \cdot)\)	580.2.s.a	30	2
580.2.u	\(\chi_{580}(81, \cdot)\)	580.2.u.a	24	6
		580.2.u.b	36
580.2.x	\(\chi_{580}(9, \cdot)\)	580.2.x.a	96	6
580.2.z	\(\chi_{580}(121, \cdot)\)	580.2.z.a	24	6
		580.2.z.b	36
580.2.ba	\(\chi_{580}(49, \cdot)\)	580.2.ba.a	84	6
580.2.bc	\(\chi_{580}(37, \cdot)\)	580.2.bc.a	180	12
580.2.be	\(\chi_{580}(19, \cdot)\)	580.2.be.a	12	12
		580.2.be.b	12
		580.2.be.c	24
		580.2.be.d	24
		580.2.be.e	960
580.2.bh	\(\chi_{580}(63, \cdot)\)	580.2.bh.a	12	12
		580.2.bh.b	12
		580.2.bh.c	1008
580.2.bi	\(\chi_{580}(7, \cdot)\)	580.2.bi.a	12	12
		580.2.bi.b	12
		580.2.bi.c	1008
580.2.bl	\(\chi_{580}(11, \cdot)\)	580.2.bl.a	360	12
		580.2.bl.b	360
580.2.bn	\(\chi_{580}(73, \cdot)\)	580.2.bn.a	180	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(580))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(580)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 2}\)