Space of modular forms of level 39 and weight 3

• Label: 39.3
• Level: 39
• Weight: 3
• Dimension: 72
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 336
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(336\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(39))\).

	Total	New	Old
Modular forms	136	92	44
Cusp forms	88	72	16
Eisenstein series	48	20	28

Trace form

72 * q - 6 * q^3 - 12 * q^4 - 6 * q^6 - 32 * q^7 - 72 * q^8 - 12 * q^9 - 72 * q^10 - 12 * q^11 - 12 * q^12 + 12 * q^13 + 48 * q^14 + 30 * q^15 + 148 * q^16 + 12 * q^17 - 96 * q^18 - 44 * q^19 - 96 * q^20 - 84 * q^21 - 192 * q^22 - 48 * q^23 - 30 * q^24 - 24 * q^25 + 60 * q^26 + 60 * q^27 + 216 * q^28 + 120 * q^29 + 426 * q^30 + 132 * q^31 + 420 * q^32 + 276 * q^33 + 420 * q^34 + 240 * q^35 + 288 * q^36 + 60 * q^37 - 126 * q^39 - 552 * q^40 - 420 * q^41 - 420 * q^42 - 524 * q^43 - 420 * q^44 - 324 * q^45 - 612 * q^46 - 192 * q^47 - 606 * q^48 - 188 * q^49 - 192 * q^50 - 324 * q^51 - 408 * q^52 - 120 * q^53 - 342 * q^54 + 48 * q^55 - 36 * q^56 + 48 * q^57 + 336 * q^58 + 204 * q^59 + 396 * q^60 + 816 * q^61 + 516 * q^62 + 384 * q^63 + 912 * q^64 + 636 * q^65 + 1104 * q^66 + 388 * q^67 + 360 * q^68 + 492 * q^69 + 720 * q^70 + 168 * q^71 + 960 * q^72 + 244 * q^73 + 156 * q^74 + 180 * q^75 + 4 * q^76 + 96 * q^78 - 192 * q^79 - 288 * q^80 - 12 * q^81 - 672 * q^82 - 252 * q^83 - 1008 * q^84 - 696 * q^85 - 1008 * q^86 - 1170 * q^87 - 1200 * q^88 - 1056 * q^89 - 2040 * q^90 - 1112 * q^91 - 600 * q^92 - 1224 * q^93 - 396 * q^94 - 720 * q^95 - 288 * q^96 + 288 * q^97 - 156 * q^98 - 84 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)

We only show spaces with odd 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
39.3.c	\(\chi_{39}(14, \cdot)\)	39.3.c.a	8	1
39.3.d	\(\chi_{39}(38, \cdot)\)	39.3.d.a	2	1
		39.3.d.b	2
		39.3.d.c	4
39.3.g	\(\chi_{39}(31, \cdot)\)	39.3.g.a	8	2
39.3.h	\(\chi_{39}(17, \cdot)\)	39.3.h.a	2	2
		39.3.h.b	12
39.3.i	\(\chi_{39}(29, \cdot)\)	39.3.i.a	2	2
		39.3.i.b	12
39.3.l	\(\chi_{39}(7, \cdot)\)	39.3.l.a	8	4
		39.3.l.b	12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(39))\) into lower level spaces

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