Space of modular forms of level 31 and weight 2

• Label: 31.2
• Level: 31
• Weight: 2
• Dimension: 26
• Nonzero newspaces: 4
• Newform subspaces: 4
• Sturm bound: 160
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(160\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(31))\).

	Total	New	Old
Modular forms	55	55	0
Cusp forms	26	26	0
Eisenstein series	29	29	0

Trace form

26 * q - 12 * q^2 - 11 * q^3 - 8 * q^4 - 9 * q^5 - 3 * q^6 - 7 * q^7 - 2 * q^9 + 3 * q^10 - 3 * q^11 + 13 * q^12 - q^13 + 9 * q^14 + 9 * q^15 + 16 * q^16 + 3 * q^17 + 24 * q^18 + 5 * q^19 + 27 * q^20 + 12 * q^21 - 9 * q^22 - 6 * q^23 - 15 * q^24 - 19 * q^25 - 3 * q^26 - 20 * q^27 - 39 * q^28 - 15 * q^29 - 18 * q^30 - 14 * q^31 - 57 * q^32 + 3 * q^33 - 21 * q^34 + 3 * q^35 - 4 * q^36 - 22 * q^37 + 15 * q^38 + 6 * q^39 + 15 * q^40 + 12 * q^41 + 51 * q^42 + 24 * q^43 + 69 * q^44 + 63 * q^45 + 57 * q^46 + 33 * q^47 + 64 * q^48 + 12 * q^49 + 3 * q^50 - 33 * q^51 + 8 * q^52 + 9 * q^53 - 60 * q^54 - 3 * q^55 - 30 * q^56 - 25 * q^57 - 30 * q^58 + 15 * q^59 - 102 * q^60 - 58 * q^61 - 12 * q^62 - 46 * q^63 - 8 * q^64 - 21 * q^65 - 96 * q^66 + 23 * q^67 + 6 * q^68 - 9 * q^69 - 6 * q^70 - 3 * q^71 + 15 * q^72 + 29 * q^73 + 24 * q^74 + 4 * q^75 + 6 * q^77 + 18 * q^78 + 30 * q^79 + 21 * q^80 + 46 * q^81 + 51 * q^82 - 36 * q^83 + 29 * q^84 + 33 * q^85 - 3 * q^86 + 45 * q^87 - 15 * q^88 - 6 * q^90 + 32 * q^91 - 42 * q^92 - 11 * q^93 + 54 * q^94 - 15 * q^95 + 12 * q^96 + 18 * q^97 - 24 * q^98 + 66 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)

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
31.2.a	\(\chi_{31}(1, \cdot)\)	31.2.a.a	2	1
31.2.c	\(\chi_{31}(5, \cdot)\)	31.2.c.a	4	2
31.2.d	\(\chi_{31}(2, \cdot)\)	31.2.d.a	4	4
31.2.g	\(\chi_{31}(7, \cdot)\)	31.2.g.a	16	8