Space of modular forms of level 240 and weight 2

• Label: 240.2
• Level: 240
• Weight: 2
• Dimension: 566
• Nonzero newspaces: 14
• Newform subspaces: 40
• Sturm bound: 6144
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 14 \)
Newform subspaces:			\( 40 \)
Sturm bound:			\(6144\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(240))\).

	Total	New	Old
Modular forms	1760	622	1138
Cusp forms	1313	566	747
Eisenstein series	447	56	391

Trace form

566 * q - 4 * q^3 + 2 * q^5 + 4 * q^7 + 24 * q^8 + 10 * q^9 - 8 * q^10 + 24 * q^11 - 8 * q^12 + 8 * q^13 - 24 * q^14 + 16 * q^15 - 64 * q^16 + 12 * q^17 - 24 * q^18 + 40 * q^19 - 16 * q^20 - 12 * q^21 - 48 * q^22 + 8 * q^23 - 64 * q^24 - 2 * q^25 - 40 * q^26 - 16 * q^27 - 80 * q^28 + 12 * q^29 - 60 * q^30 - 72 * q^31 - 80 * q^32 - 28 * q^33 - 128 * q^34 - 48 * q^35 - 64 * q^36 - 32 * q^37 - 96 * q^38 - 68 * q^39 - 152 * q^40 - 52 * q^41 - 44 * q^43 - 32 * q^44 - 22 * q^45 - 64 * q^46 - 24 * q^47 + 56 * q^48 - 6 * q^49 - 64 * q^50 - 112 * q^51 - 16 * q^52 - 44 * q^53 + 88 * q^54 - 64 * q^55 - 12 * q^57 - 48 * q^58 - 56 * q^59 + 16 * q^60 - 148 * q^61 + 24 * q^62 - 128 * q^63 - 96 * q^64 + 4 * q^65 - 56 * q^66 - 164 * q^67 + 48 * q^68 - 112 * q^69 + 56 * q^70 - 144 * q^71 + 40 * q^72 - 56 * q^73 + 72 * q^74 - 144 * q^75 - 32 * q^76 - 80 * q^77 + 64 * q^78 - 168 * q^79 + 152 * q^80 - 66 * q^81 + 64 * q^82 - 104 * q^83 + 160 * q^84 - 40 * q^85 + 160 * q^86 - 8 * q^87 + 224 * q^88 + 52 * q^89 + 136 * q^90 + 40 * q^91 + 176 * q^92 + 24 * q^93 + 176 * q^94 - 16 * q^95 + 160 * q^96 + 88 * q^97 + 128 * q^98 + 48 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)

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
240.2.a	\(\chi_{240}(1, \cdot)\)	240.2.a.a	1	1
		240.2.a.b	1
		240.2.a.c	1
		240.2.a.d	1
240.2.b	\(\chi_{240}(71, \cdot)\)	None	0	1
240.2.d	\(\chi_{240}(169, \cdot)\)	None	0	1
240.2.f	\(\chi_{240}(49, \cdot)\)	240.2.f.a	2	1
		240.2.f.b	2
		240.2.f.c	2
240.2.h	\(\chi_{240}(191, \cdot)\)	240.2.h.a	4	1
		240.2.h.b	4
240.2.k	\(\chi_{240}(121, \cdot)\)	None	0	1
240.2.m	\(\chi_{240}(119, \cdot)\)	None	0	1
240.2.o	\(\chi_{240}(239, \cdot)\)	240.2.o.a	4	1
		240.2.o.b	8
240.2.s	\(\chi_{240}(61, \cdot)\)	240.2.s.a	4	2
		240.2.s.b	8
		240.2.s.c	20
240.2.t	\(\chi_{240}(59, \cdot)\)	240.2.t.a	8	2
		240.2.t.b	80
240.2.v	\(\chi_{240}(17, \cdot)\)	240.2.v.a	4	2
		240.2.v.b	4
		240.2.v.c	4
		240.2.v.d	4
		240.2.v.e	4
240.2.w	\(\chi_{240}(127, \cdot)\)	240.2.w.a	4	2
		240.2.w.b	8
240.2.y	\(\chi_{240}(163, \cdot)\)	240.2.y.a	2	2
		240.2.y.b	2
		240.2.y.c	2
		240.2.y.d	6
		240.2.y.e	16
		240.2.y.f	20
240.2.bb	\(\chi_{240}(173, \cdot)\)	240.2.bb.a	88	2
240.2.bc	\(\chi_{240}(43, \cdot)\)	240.2.bc.a	2	2
		240.2.bc.b	2
		240.2.bc.c	2
		240.2.bc.d	6
		240.2.bc.e	16
		240.2.bc.f	20
240.2.bf	\(\chi_{240}(53, \cdot)\)	240.2.bf.a	88	2
240.2.bh	\(\chi_{240}(7, \cdot)\)	None	0	2
240.2.bi	\(\chi_{240}(137, \cdot)\)	None	0	2
240.2.bk	\(\chi_{240}(11, \cdot)\)	240.2.bk.a	4	2
		240.2.bk.b	60
240.2.bl	\(\chi_{240}(109, \cdot)\)	240.2.bl.a	48	2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(240))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(240)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)