Space of modular forms of level 130 and weight 2

• Label: 130.2
• Level: 130
• Weight: 2
• Dimension: 155
• Nonzero newspaces: 12
• Newform subspaces: 30
• Sturm bound: 2016
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 30 \)
Sturm bound:			\(2016\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(130))\).

	Total	New	Old
Modular forms	600	155	445
Cusp forms	409	155	254
Eisenstein series	191	0	191

Trace form

155 * q + q^2 + 4 * q^3 + q^4 + q^5 + 4 * q^6 - 5 * q^8 - 19 * q^9 - 14 * q^10 - 12 * q^11 - 4 * q^12 - 35 * q^13 - 16 * q^14 - 20 * q^15 - 7 * q^16 - 12 * q^17 - 17 * q^18 - 36 * q^19 - 2 * q^20 - 24 * q^21 + 12 * q^22 + 4 * q^24 + q^25 + 13 * q^26 - 32 * q^27 - 48 * q^29 - 20 * q^30 - 48 * q^31 + q^32 - 72 * q^33 - 30 * q^34 - 64 * q^35 - 35 * q^36 - 24 * q^37 - 52 * q^38 - 52 * q^39 + q^40 - 60 * q^41 - 40 * q^42 - 44 * q^43 - 36 * q^44 - 62 * q^45 - 24 * q^46 - 48 * q^47 + 4 * q^48 - 7 * q^49 - 14 * q^50 + 24 * q^51 + 11 * q^52 + 78 * q^53 + 112 * q^54 + 96 * q^55 + 32 * q^56 + 192 * q^57 + 84 * q^58 + 108 * q^59 + 76 * q^60 + 80 * q^61 + 104 * q^62 + 192 * q^63 + 7 * q^64 + 118 * q^65 + 144 * q^66 + 108 * q^67 + 24 * q^68 + 192 * q^69 + 116 * q^70 + 24 * q^71 + 61 * q^72 + 42 * q^73 + 68 * q^74 + 116 * q^75 + 12 * q^76 + 76 * q^78 - 16 * q^79 + 10 * q^80 - 31 * q^81 - 48 * q^82 - 108 * q^83 - 24 * q^84 - 105 * q^85 - 4 * q^86 - 120 * q^87 + 12 * q^88 - 102 * q^89 - 47 * q^90 - 48 * q^91 - 24 * q^92 - 96 * q^93 - 72 * q^94 - 52 * q^95 + 4 * q^96 - 102 * q^97 - 39 * q^98 - 60 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)

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
130.2.a	\(\chi_{130}(1, \cdot)\)	130.2.a.a	1	1
		130.2.a.b	1
		130.2.a.c	1
130.2.b	\(\chi_{130}(79, \cdot)\)	130.2.b.a	6	1
130.2.c	\(\chi_{130}(129, \cdot)\)	130.2.c.a	4	1
		130.2.c.b	4
130.2.d	\(\chi_{130}(51, \cdot)\)	130.2.d.a	2	1
130.2.e	\(\chi_{130}(61, \cdot)\)	130.2.e.a	2	2
		130.2.e.b	2
		130.2.e.c	4
		130.2.e.d	4
130.2.g	\(\chi_{130}(57, \cdot)\)	130.2.g.a	2	2
		130.2.g.b	2
		130.2.g.c	2
		130.2.g.d	4
		130.2.g.e	4
130.2.j	\(\chi_{130}(47, \cdot)\)	130.2.j.a	2	2
		130.2.j.b	2
		130.2.j.c	2
		130.2.j.d	4
		130.2.j.e	4
130.2.l	\(\chi_{130}(101, \cdot)\)	130.2.l.a	4	2
		130.2.l.b	8
130.2.m	\(\chi_{130}(49, \cdot)\)	130.2.m.a	8	2
		130.2.m.b	8
130.2.n	\(\chi_{130}(9, \cdot)\)	130.2.n.a	12	2
130.2.p	\(\chi_{130}(7, \cdot)\)	130.2.p.a	12	4
		130.2.p.b	16
130.2.s	\(\chi_{130}(33, \cdot)\)	130.2.s.a	12	4
		130.2.s.b	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(130))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(130)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)