Space of modular forms of level 680 and weight 2

• Label: 680.2
• Level: 680
• Weight: 2
• Dimension: 6898
• Nonzero newspaces: 28
• Newform subspaces: 63
• Sturm bound: 55296
• Trace bound: 27

Defining parameters

Level:	\( N \)	=	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Newform subspaces:			\( 63 \)
Sturm bound:			\(55296\)
Trace bound:			\(27\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(680))\).

	Total	New	Old
Modular forms	14592	7258	7334
Cusp forms	13057	6898	6159
Eisenstein series	1535	360	1175

Trace form

6898 * q - 24 * q^2 - 24 * q^3 - 24 * q^4 + 2 * q^5 - 80 * q^6 - 16 * q^7 - 24 * q^8 - 38 * q^9 - 40 * q^10 - 72 * q^11 - 48 * q^12 + 4 * q^13 - 48 * q^14 - 56 * q^15 - 112 * q^16 - 58 * q^17 - 112 * q^18 - 56 * q^19 - 80 * q^20 - 16 * q^21 - 64 * q^22 - 32 * q^23 - 80 * q^24 - 50 * q^25 - 112 * q^26 - 16 * q^28 + 52 * q^29 - 48 * q^30 - 32 * q^31 + 16 * q^32 + 16 * q^33 + 4 * q^34 - 80 * q^35 - 16 * q^36 + 52 * q^37 + 16 * q^38 + 16 * q^39 + 40 * q^40 - 116 * q^41 + 16 * q^42 - 24 * q^43 + 22 * q^45 - 32 * q^46 - 80 * q^47 - 112 * q^48 - 78 * q^49 - 80 * q^50 - 104 * q^51 - 104 * q^52 - 36 * q^53 - 240 * q^54 - 152 * q^55 - 352 * q^56 - 144 * q^57 - 344 * q^58 - 168 * q^59 - 336 * q^60 - 52 * q^61 - 368 * q^62 - 304 * q^63 - 288 * q^64 - 136 * q^65 - 544 * q^66 - 120 * q^67 - 404 * q^68 - 208 * q^69 - 224 * q^70 - 144 * q^71 - 424 * q^72 - 140 * q^73 - 184 * q^74 - 40 * q^75 - 320 * q^76 - 64 * q^77 - 320 * q^78 + 32 * q^79 - 112 * q^80 - 246 * q^81 - 120 * q^82 + 8 * q^83 - 128 * q^84 + 18 * q^85 - 208 * q^86 + 160 * q^87 - 32 * q^88 + 4 * q^89 - 120 * q^90 + 64 * q^91 + 128 * q^93 - 96 * q^94 + 56 * q^95 - 192 * q^96 + 28 * q^97 - 56 * q^98 + 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(680))\)

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
680.2.a	\(\chi_{680}(1, \cdot)\)	680.2.a.a	1	1
		680.2.a.b	1
		680.2.a.c	1
		680.2.a.d	2
		680.2.a.e	2
		680.2.a.f	3
		680.2.a.g	3
		680.2.a.h	3
680.2.c	\(\chi_{680}(441, \cdot)\)	680.2.c.a	2	1
		680.2.c.b	8
		680.2.c.c	8
680.2.e	\(\chi_{680}(409, \cdot)\)	680.2.e.a	2	1
		680.2.e.b	10
		680.2.e.c	12
680.2.f	\(\chi_{680}(341, \cdot)\)	680.2.f.a	2	1
		680.2.f.b	2
		680.2.f.c	6
		680.2.f.d	24
		680.2.f.e	30
680.2.h	\(\chi_{680}(509, \cdot)\)	680.2.h.a	16	1
		680.2.h.b	40
		680.2.h.c	48
680.2.j	\(\chi_{680}(69, \cdot)\)	680.2.j.a	2	1
		680.2.j.b	2
		680.2.j.c	4
		680.2.j.d	4
		680.2.j.e	84
680.2.l	\(\chi_{680}(101, \cdot)\)	680.2.l.a	36	1
		680.2.l.b	36
680.2.o	\(\chi_{680}(169, \cdot)\)	680.2.o.a	4	1
		680.2.o.b	24
680.2.q	\(\chi_{680}(47, \cdot)\)	None	0	2
680.2.t	\(\chi_{680}(523, \cdot)\)	680.2.t.a	208	2
680.2.u	\(\chi_{680}(67, \cdot)\)	680.2.u.a	8	2
		680.2.u.b	8
		680.2.u.c	8
		680.2.u.d	184
680.2.x	\(\chi_{680}(103, \cdot)\)	None	0	2
680.2.z	\(\chi_{680}(89, \cdot)\)	680.2.z.a	2	2
		680.2.z.b	2
		680.2.z.c	26
		680.2.z.d	26
680.2.ba	\(\chi_{680}(21, \cdot)\)	680.2.ba.a	4	2
		680.2.ba.b	140
680.2.bd	\(\chi_{680}(81, \cdot)\)	680.2.bd.a	16	2
		680.2.bd.b	20
680.2.be	\(\chi_{680}(149, \cdot)\)	680.2.be.a	208	2
680.2.bg	\(\chi_{680}(307, \cdot)\)	680.2.bg.a	192	2
680.2.bj	\(\chi_{680}(407, \cdot)\)	None	0	2
680.2.bl	\(\chi_{680}(123, \cdot)\)	680.2.bl.a	208	2
680.2.bm	\(\chi_{680}(183, \cdot)\)	None	0	2
680.2.bo	\(\chi_{680}(121, \cdot)\)	680.2.bo.a	32	4
		680.2.bo.b	40
680.2.br	\(\chi_{680}(189, \cdot)\)	680.2.br.a	416	4
680.2.bs	\(\chi_{680}(127, \cdot)\)	None	0	4
680.2.bv	\(\chi_{680}(87, \cdot)\)	None	0	4
680.2.bw	\(\chi_{680}(43, \cdot)\)	680.2.bw.a	416	4
680.2.bz	\(\chi_{680}(83, \cdot)\)	680.2.bz.a	416	4
680.2.cb	\(\chi_{680}(9, \cdot)\)	680.2.cb.a	52	4
		680.2.cb.b	52
680.2.cc	\(\chi_{680}(461, \cdot)\)	680.2.cc.a	288	4
680.2.cf	\(\chi_{680}(37, \cdot)\)	680.2.cf.a	832	8
680.2.cg	\(\chi_{680}(57, \cdot)\)	680.2.cg.a	104	8
		680.2.cg.b	112
680.2.ci	\(\chi_{680}(11, \cdot)\)	680.2.ci.a	576	8
680.2.cl	\(\chi_{680}(31, \cdot)\)	None	0	8
680.2.cn	\(\chi_{680}(39, \cdot)\)	None	0	8
680.2.co	\(\chi_{680}(99, \cdot)\)	680.2.co.a	832	8
680.2.cq	\(\chi_{680}(97, \cdot)\)	680.2.cq.a	104	8
		680.2.cq.b	112
680.2.ct	\(\chi_{680}(133, \cdot)\)	680.2.ct.a	832	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(680))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(680)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 2}\)