Space of modular forms of level 38 and weight 4

• Label: 38.4
• Level: 38
• Weight: 4
• Dimension: 45
• Nonzero newspaces: 3
• Newform subspaces: 8
• Sturm bound: 360
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(360\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(38))\).

	Total	New	Old
Modular forms	153	45	108
Cusp forms	117	45	72
Eisenstein series	36	0	36

Trace form

45 * q + 144 * q^12 + 288 * q^13 + 36 * q^14 - 216 * q^15 - 288 * q^17 - 486 * q^18 - 756 * q^19 - 288 * q^20 - 504 * q^21 - 162 * q^22 + 36 * q^23 + 864 * q^25 + 684 * q^26 + 1953 * q^27 + 432 * q^28 + 630 * q^29 + 90 * q^31 - 918 * q^33 - 1116 * q^35 - 666 * q^37 - 1890 * q^39 - 450 * q^41 + 504 * q^43 + 900 * q^44 + 5130 * q^45 + 1944 * q^46 + 2790 * q^47 + 144 * q^48 + 1710 * q^49 - 1008 * q^50 - 1035 * q^51 - 216 * q^52 - 3168 * q^53 - 2700 * q^54 - 3888 * q^55 - 2016 * q^56 - 5040 * q^57 - 1944 * q^58 - 4500 * q^59 - 1584 * q^60 - 1782 * q^61 - 1404 * q^62 + 936 * q^63 + 2070 * q^65 + 2448 * q^66 + 2160 * q^67 + 684 * q^68 + 5400 * q^69 + 4536 * q^70 + 7326 * q^71 + 1656 * q^72 - 567 * q^73 - 3150 * q^75 + 2502 * q^77 + 6408 * q^78 + 2610 * q^79 + 5121 * q^81 + 2232 * q^82 + 1710 * q^83 + 864 * q^84 - 288 * q^85 - 792 * q^86 - 3420 * q^87 - 1530 * q^89 - 6660 * q^90 - 1944 * q^91 - 3168 * q^92 - 11862 * q^93 - 6768 * q^94 + 3168 * q^95 + 972 * q^97 - 5904 * q^98 - 4545 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)

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
38.4.a	\(\chi_{38}(1, \cdot)\)	38.4.a.a	1	1
		38.4.a.b	2
		38.4.a.c	2
38.4.c	\(\chi_{38}(7, \cdot)\)	38.4.c.a	2	2
		38.4.c.b	2
		38.4.c.c	6
38.4.e	\(\chi_{38}(5, \cdot)\)	38.4.e.a	12	6
		38.4.e.b	18

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

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