Space of modular forms of level 131 and weight 2

• Label: 131.2
• Level: 131
• Weight: 2
• Dimension: 651
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 2860
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 131 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(2860\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(131))\).

	Total	New	Old
Modular forms	780	780	0
Cusp forms	651	651	0
Eisenstein series	129	129	0

Trace form

651 * q - 62 * q^2 - 61 * q^3 - 58 * q^4 - 59 * q^5 - 53 * q^6 - 57 * q^7 - 50 * q^8 - 52 * q^9 - 47 * q^10 - 53 * q^11 - 37 * q^12 - 51 * q^13 - 41 * q^14 - 41 * q^15 - 34 * q^16 - 47 * q^17 - 26 * q^18 - 45 * q^19 - 23 * q^20 - 33 * q^21 - 29 * q^22 - 41 * q^23 - 5 * q^24 - 34 * q^25 - 23 * q^26 - 25 * q^27 - 9 * q^28 - 35 * q^29 + 7 * q^30 - 33 * q^31 - 2 * q^32 - 17 * q^33 - 11 * q^34 - 17 * q^35 + 26 * q^36 - 27 * q^37 - 5 * q^38 - 9 * q^39 + 25 * q^40 - 23 * q^41 + 31 * q^42 - 21 * q^43 + 19 * q^44 + 13 * q^45 + 7 * q^46 - 17 * q^47 + 59 * q^48 - 8 * q^49 + 28 * q^50 + 7 * q^51 + 33 * q^52 - 11 * q^53 + 55 * q^54 + 7 * q^55 + 55 * q^56 + 15 * q^57 + 25 * q^58 - 5 * q^59 + 103 * q^60 - 3 * q^61 + 31 * q^62 + 39 * q^63 + 62 * q^64 + 19 * q^65 + 79 * q^66 + 3 * q^67 + 61 * q^68 + 31 * q^69 + 79 * q^70 + 7 * q^71 + 130 * q^72 + 9 * q^73 + 49 * q^74 + 59 * q^75 + 75 * q^76 + 31 * q^77 + 103 * q^78 + 15 * q^79 + 121 * q^80 + 56 * q^81 + 61 * q^82 + 19 * q^83 + 159 * q^84 + 43 * q^85 + 67 * q^86 + 55 * q^87 + 115 * q^88 + 25 * q^89 + 169 * q^90 + 47 * q^91 + 103 * q^92 + 63 * q^93 + 79 * q^94 + 55 * q^95 + 187 * q^96 + 33 * q^97 + 106 * q^98 + 91 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(131))\)

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
131.2.a	\(\chi_{131}(1, \cdot)\)	131.2.a.a	1	1
		131.2.a.b	10
131.2.c	\(\chi_{131}(53, \cdot)\)	131.2.c.a	4	4
		131.2.c.b	4
		131.2.c.c	32
131.2.e	\(\chi_{131}(39, \cdot)\)	131.2.e.a	120	12
131.2.g	\(\chi_{131}(3, \cdot)\)	131.2.g.a	480	48