Space of modular forms of level 38 and weight 2

• Label: 38.2
• Level: 38
• Weight: 2
• Dimension: 14
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 180
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(180\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(38))\).

	Total	New	Old
Modular forms	63	14	49
Cusp forms	28	14	14
Eisenstein series	35	0	35

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)

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
38.2.a	\(\chi_{38}(1, \cdot)\)	38.2.a.a	1	1
		38.2.a.b	1
38.2.c	\(\chi_{38}(7, \cdot)\)	38.2.c.a	2	2
		38.2.c.b	4
38.2.e	\(\chi_{38}(5, \cdot)\)	38.2.e.a	6	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)