Space of modular forms of level 39 and weight 6

• Label: 39.6
• Level: 39
• Weight: 6
• Dimension: 196
• Nonzero newspaces: 6
• Newform subspaces: 13
• Sturm bound: 672
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 13 \)
Sturm bound:			\(672\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(39))\).

	Total	New	Old
Modular forms	304	220	84
Cusp forms	256	196	60
Eisenstein series	48	24	24

Trace form

196 * q + 12 * q^2 - 24 * q^3 - 20 * q^4 - 12 * q^5 + 102 * q^6 + 664 * q^7 - 1488 * q^8 - 330 * q^9 - 60 * q^10 + 2196 * q^11 + 2808 * q^12 + 2494 * q^13 + 576 * q^14 - 1302 * q^15 - 7980 * q^16 + 630 * q^17 + 444 * q^18 - 8876 * q^19 - 11040 * q^20 - 2952 * q^21 - 8520 * q^22 + 8136 * q^23 + 21018 * q^24 + 24928 * q^25 + 39768 * q^26 + 13686 * q^27 + 7232 * q^28 - 18126 * q^29 - 15822 * q^30 - 34996 * q^31 - 79620 * q^32 - 3780 * q^33 - 15588 * q^34 + 17880 * q^35 + 8748 * q^36 + 41534 * q^37 - 6672 * q^38 + 3804 * q^39 + 80568 * q^40 - 12258 * q^41 - 70728 * q^42 - 167204 * q^43 - 123348 * q^44 + 36990 * q^45 - 95172 * q^46 + 47376 * q^47 + 154314 * q^48 + 191354 * q^49 + 285936 * q^50 + 108972 * q^51 + 313720 * q^52 + 47172 * q^53 - 109290 * q^54 - 67752 * q^55 - 287412 * q^56 - 142752 * q^57 - 296028 * q^58 - 155364 * q^59 - 214056 * q^60 - 439918 * q^61 + 35892 * q^62 + 17004 * q^63 + 328264 * q^64 + 375342 * q^65 + 658920 * q^66 + 475756 * q^67 + 138384 * q^68 + 182052 * q^69 - 63600 * q^70 - 63384 * q^71 - 386292 * q^72 - 26120 * q^73 - 51696 * q^74 - 357426 * q^75 - 482732 * q^76 - 372648 * q^77 - 846696 * q^78 - 333040 * q^79 - 275136 * q^80 + 71418 * q^81 - 363180 * q^82 - 269700 * q^83 + 352896 * q^84 + 628062 * q^85 + 1069920 * q^86 + 743238 * q^87 + 1093008 * q^88 + 123972 * q^89 + 200232 * q^90 - 546344 * q^91 - 26136 * q^92 - 682980 * q^93 - 389196 * q^94 - 486408 * q^95 - 1121868 * q^96 - 674884 * q^97 - 117120 * q^98 + 465840 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(39))\)

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
39.6.a	\(\chi_{39}(1, \cdot)\)	39.6.a.a	1	1
		39.6.a.b	2
		39.6.a.c	3
		39.6.a.d	4
39.6.b	\(\chi_{39}(25, \cdot)\)	39.6.b.a	4	1
		39.6.b.b	6
39.6.e	\(\chi_{39}(16, \cdot)\)	39.6.e.a	12	2
		39.6.e.b	14
39.6.f	\(\chi_{39}(5, \cdot)\)	39.6.f.a	44	2
39.6.j	\(\chi_{39}(4, \cdot)\)	39.6.j.a	10	2
		39.6.j.b	12
39.6.k	\(\chi_{39}(2, \cdot)\)	39.6.k.a	4	4
		39.6.k.b	80

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(39))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(39)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)