Space of modular forms of level 340 and weight 2

• Label: 340.2
• Level: 340
• Weight: 2
• Dimension: 1746
• Nonzero newspaces: 18
• Newform subspaces: 36
• Sturm bound: 13824
• Trace bound: 27

Defining parameters

Level:	\( N \)	=	\( 340 = 2^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 36 \)
Sturm bound:			\(13824\)
Trace bound:			\(27\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(340))\).

	Total	New	Old
Modular forms	3776	1922	1854
Cusp forms	3137	1746	1391
Eisenstein series	639	176	463

Trace form

1746 * q - 12 * q^2 + 4 * q^3 - 16 * q^4 - 38 * q^5 - 48 * q^6 - 4 * q^7 - 24 * q^8 - 34 * q^9 - 36 * q^10 + 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 + 20 * q^15 - 48 * q^16 - 16 * q^17 - 20 * q^18 + 24 * q^19 - 16 * q^20 - 40 * q^21 - 16 * q^22 + 4 * q^23 - 48 * q^24 - 74 * q^25 - 120 * q^26 - 56 * q^27 - 112 * q^28 - 84 * q^29 - 88 * q^30 - 56 * q^31 - 112 * q^32 - 128 * q^33 - 144 * q^34 - 28 * q^35 - 200 * q^36 - 72 * q^37 - 96 * q^38 - 24 * q^39 - 80 * q^40 - 68 * q^41 - 112 * q^42 + 4 * q^43 - 80 * q^44 - 46 * q^45 - 80 * q^46 + 92 * q^47 + 32 * q^48 + 38 * q^49 - 4 * q^50 + 52 * q^51 - 24 * q^52 - 16 * q^53 + 16 * q^54 + 16 * q^55 + 32 * q^56 - 144 * q^57 + 80 * q^58 + 8 * q^59 + 80 * q^60 - 212 * q^61 + 96 * q^62 - 52 * q^63 + 80 * q^64 - 140 * q^65 + 128 * q^66 - 36 * q^67 + 172 * q^68 - 264 * q^69 + 48 * q^70 - 40 * q^71 + 216 * q^72 - 288 * q^73 + 80 * q^74 - 140 * q^75 + 64 * q^76 - 192 * q^77 + 192 * q^78 - 112 * q^79 - 40 * q^80 - 310 * q^81 + 32 * q^82 - 108 * q^83 - 224 * q^85 - 256 * q^86 - 168 * q^87 - 144 * q^88 - 164 * q^89 - 116 * q^90 - 232 * q^91 - 240 * q^92 - 240 * q^93 - 208 * q^94 - 184 * q^95 - 352 * q^96 - 216 * q^97 - 316 * q^98 - 192 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(340))\)

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
340.2.a	\(\chi_{340}(1, \cdot)\)	340.2.a.a	1	1
		340.2.a.b	3
340.2.c	\(\chi_{340}(101, \cdot)\)	340.2.c.a	6	1
340.2.e	\(\chi_{340}(69, \cdot)\)	340.2.e.a	8	1
340.2.g	\(\chi_{340}(169, \cdot)\)	340.2.g.a	8	1
340.2.i	\(\chi_{340}(47, \cdot)\)	340.2.i.a	2	2
		340.2.i.b	2
		340.2.i.c	96
340.2.l	\(\chi_{340}(103, \cdot)\)	340.2.l.a	8	2
		340.2.l.b	88
340.2.m	\(\chi_{340}(89, \cdot)\)	340.2.m.a	2	2
		340.2.m.b	2
		340.2.m.c	12
340.2.o	\(\chi_{340}(21, \cdot)\)	340.2.o.a	12	2
340.2.r	\(\chi_{340}(67, \cdot)\)	340.2.r.a	2	2
		340.2.r.b	2
		340.2.r.c	96
340.2.s	\(\chi_{340}(183, \cdot)\)	340.2.s.a	2	2
		340.2.s.b	2
		340.2.s.c	96
340.2.u	\(\chi_{340}(121, \cdot)\)	340.2.u.a	24	4
340.2.w	\(\chi_{340}(83, \cdot)\)	340.2.w.a	4	4
		340.2.w.b	4
		340.2.w.c	8
		340.2.w.d	184
340.2.z	\(\chi_{340}(43, \cdot)\)	340.2.z.a	4	4
		340.2.z.b	4
		340.2.z.c	8
		340.2.z.d	184
340.2.bb	\(\chi_{340}(9, \cdot)\)	340.2.bb.a	40	4
340.2.bd	\(\chi_{340}(57, \cdot)\)	340.2.bd.a	72	8
340.2.bf	\(\chi_{340}(11, \cdot)\)	340.2.bf.a	288	8
340.2.bg	\(\chi_{340}(39, \cdot)\)	340.2.bg.a	8	8
		340.2.bg.b	8
		340.2.bg.c	384
340.2.bi	\(\chi_{340}(37, \cdot)\)	340.2.bi.a	72	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(340))\) into lower level spaces

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