Space of modular forms of level 37 and weight 2

• Label: 37.2
• Level: 37
• Weight: 2
• Dimension: 40
• Nonzero newspaces: 6
• Newform subspaces: 8
• Sturm bound: 228
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(228\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(37))\).

	Total	New	Old
Modular forms	75	75	0
Cusp forms	40	40	0
Eisenstein series	35	35	0

Trace form

40 * q - 15 * q^2 - 14 * q^3 - 11 * q^4 - 12 * q^5 - 6 * q^6 - 10 * q^7 - 3 * q^8 - 5 * q^9 - 6 * q^11 + 10 * q^12 - 4 * q^13 + 6 * q^14 + 6 * q^15 + 13 * q^16 + 21 * q^18 + 2 * q^19 + 24 * q^20 + 14 * q^21 + 18 * q^22 + 6 * q^23 + 42 * q^24 + 13 * q^25 + 15 * q^26 - 2 * q^27 - 22 * q^28 - 6 * q^29 - 18 * q^30 - 40 * q^31 - 27 * q^32 - 6 * q^33 - 36 * q^34 - 24 * q^35 - 80 * q^36 - 23 * q^37 - 12 * q^38 - 4 * q^39 - 63 * q^40 - 30 * q^41 + 6 * q^42 - 10 * q^43 - 6 * q^44 + 6 * q^45 - 18 * q^46 + 12 * q^47 + 46 * q^48 + 15 * q^49 + 66 * q^50 + 54 * q^51 + 80 * q^52 + 36 * q^53 + 102 * q^54 + 54 * q^55 + 102 * q^56 + 62 * q^57 + 54 * q^58 + 6 * q^59 + 24 * q^60 - q^61 - 12 * q^62 - 22 * q^63 - 17 * q^64 - 15 * q^65 - 126 * q^66 + 14 * q^67 - 66 * q^69 - 72 * q^70 - 18 * q^71 - 111 * q^72 - 34 * q^73 - 51 * q^74 - 92 * q^75 - 58 * q^76 + 6 * q^77 - 102 * q^78 - 10 * q^79 - 30 * q^80 - 41 * q^81 + 30 * q^83 - 46 * q^84 + 9 * q^85 - 12 * q^86 - 6 * q^87 + 72 * q^88 + 27 * q^89 + 90 * q^90 + 52 * q^91 + 60 * q^92 + 56 * q^93 + 54 * q^94 + 30 * q^95 + 54 * q^96 + 8 * q^97 + 9 * q^98 + 48 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)

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
37.2.a	\(\chi_{37}(1, \cdot)\)	37.2.a.a	1	1
		37.2.a.b	1
37.2.b	\(\chi_{37}(36, \cdot)\)	37.2.b.a	2	1
37.2.c	\(\chi_{37}(10, \cdot)\)	37.2.c.a	2	2
37.2.e	\(\chi_{37}(11, \cdot)\)	37.2.e.a	4	2
37.2.f	\(\chi_{37}(7, \cdot)\)	37.2.f.a	6	6
		37.2.f.b	6
37.2.h	\(\chi_{37}(3, \cdot)\)	37.2.h.a	18	6