Space of modular forms of level 39 and weight 4

• Label: 39.4
• Level: 39
• Weight: 4
• Dimension: 114
• Nonzero newspaces: 6
• Newform subspaces: 14
• Sturm bound: 448
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(448\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(39))\).

	Total	New	Old
Modular forms	192	138	54
Cusp forms	144	114	30
Eisenstein series	48	24	24

Trace form

114 * q - 6 * q^3 - 12 * q^4 - 6 * q^6 + 60 * q^7 + 144 * q^8 - 6 * q^9 - 192 * q^10 - 120 * q^11 - 240 * q^12 - 300 * q^13 - 240 * q^14 - 78 * q^15 - 12 * q^16 + 378 * q^17 + 660 * q^18 + 876 * q^19 + 1032 * q^20 - 6 * q^21 - 792 * q^22 - 456 * q^23 - 1158 * q^24 - 750 * q^25 - 1500 * q^26 - 840 * q^27 - 1056 * q^28 - 390 * q^29 - 1062 * q^30 + 108 * q^31 + 1020 * q^32 + 882 * q^33 + 2244 * q^34 + 1560 * q^35 + 3060 * q^36 + 630 * q^37 + 1746 * q^39 + 3864 * q^40 + 2478 * q^41 + 2496 * q^42 + 1332 * q^43 + 300 * q^44 - 288 * q^45 - 2532 * q^46 - 1488 * q^47 - 3366 * q^48 - 3972 * q^49 - 4416 * q^50 - 2448 * q^51 - 1656 * q^52 - 1896 * q^53 + 1698 * q^54 - 2820 * q^55 - 2772 * q^56 - 1170 * q^57 - 2064 * q^58 - 984 * q^59 - 2664 * q^60 + 2250 * q^61 - 636 * q^62 - 5154 * q^63 + 1800 * q^64 + 2430 * q^65 - 2472 * q^66 + 228 * q^67 - 4680 * q^68 - 1674 * q^69 - 960 * q^70 - 528 * q^71 + 3084 * q^72 + 1140 * q^73 + 5772 * q^74 + 7896 * q^75 + 12468 * q^76 + 6624 * q^77 + 14604 * q^78 + 5496 * q^79 + 9312 * q^80 + 5610 * q^81 - 288 * q^82 - 1224 * q^83 + 3600 * q^84 - 30 * q^85 + 6384 * q^86 + 2646 * q^87 - 3888 * q^88 + 3480 * q^89 - 2160 * q^90 + 396 * q^91 - 6360 * q^92 - 7554 * q^93 - 10620 * q^94 - 7080 * q^95 - 17244 * q^96 - 11028 * q^97 - 9516 * q^98 - 11394 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)

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
39.4.a	\(\chi_{39}(1, \cdot)\)	39.4.a.a	1	1
		39.4.a.b	2
		39.4.a.c	3
39.4.b	\(\chi_{39}(25, \cdot)\)	39.4.b.a	4	1
		39.4.b.b	4
39.4.e	\(\chi_{39}(16, \cdot)\)	39.4.e.a	2	2
		39.4.e.b	2
		39.4.e.c	8
39.4.f	\(\chi_{39}(5, \cdot)\)	39.4.f.a	4	2
		39.4.f.b	20
39.4.j	\(\chi_{39}(4, \cdot)\)	39.4.j.a	2	2
		39.4.j.b	4
		39.4.j.c	10
39.4.k	\(\chi_{39}(2, \cdot)\)	39.4.k.a	48	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(39))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(39)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)