Space of modular forms of level 130 and weight 6

• Label: 130.6
• Level: 130
• Weight: 6
• Dimension: 760
• Nonzero newspaces: 12
• Sturm bound: 6048
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(6048\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(130))\).

	Total	New	Old
Modular forms	2616	760	1856
Cusp forms	2424	760	1664
Eisenstein series	192	0	192

Trace form

760 * q + 8 * q^2 - 8 * q^3 - 32 * q^4 - 170 * q^5 + 160 * q^6 - 568 * q^7 + 512 * q^8 + 1286 * q^9 + 420 * q^10 - 656 * q^11 - 1280 * q^12 - 6402 * q^13 - 4192 * q^14 + 736 * q^15 - 512 * q^16 + 102 * q^17 + 17504 * q^18 + 21632 * q^19 + 2352 * q^20 - 584 * q^21 - 6624 * q^22 - 12744 * q^23 - 4608 * q^24 - 15450 * q^25 - 2920 * q^26 - 19352 * q^27 - 9088 * q^28 - 14250 * q^29 + 41856 * q^30 + 118384 * q^31 + 2048 * q^32 + 61464 * q^33 - 27056 * q^34 - 35080 * q^35 - 57120 * q^36 - 73426 * q^37 - 69248 * q^38 - 144128 * q^39 + 640 * q^40 - 54386 * q^41 - 23072 * q^42 + 89680 * q^43 + 77696 * q^44 + 138735 * q^45 + 105920 * q^46 + 96960 * q^47 - 2048 * q^48 + 72574 * q^49 + 86980 * q^50 - 218368 * q^51 - 80320 * q^52 - 49596 * q^53 - 172128 * q^54 - 426356 * q^55 - 53760 * q^56 - 248512 * q^57 - 161256 * q^58 - 94664 * q^59 + 26112 * q^60 + 385390 * q^61 + 265888 * q^62 + 543944 * q^63 + 16384 * q^64 + 743315 * q^65 + 486400 * q^66 + 364256 * q^67 - 19680 * q^68 - 11312 * q^69 - 339952 * q^70 - 175104 * q^71 - 93568 * q^72 - 806044 * q^73 - 680392 * q^74 - 1525480 * q^75 - 241408 * q^76 - 512256 * q^77 + 119264 * q^78 + 967296 * q^79 + 50944 * q^80 + 1479390 * q^81 + 689976 * q^82 + 744024 * q^83 + 318336 * q^84 + 31189 * q^85 + 11808 * q^86 - 412128 * q^87 - 105984 * q^88 - 198628 * q^89 - 539880 * q^90 - 755368 * q^91 - 454656 * q^92 - 637456 * q^93 - 233056 * q^94 - 259664 * q^95 + 40960 * q^96 - 313204 * q^97 - 687288 * q^98 + 1253360 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(130))\)

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
130.6.a	\(\chi_{130}(1, \cdot)\)	130.6.a.a	2	1
		130.6.a.b	2
		130.6.a.c	2
		130.6.a.d	2
		130.6.a.e	2
		130.6.a.f	3
		130.6.a.g	3
		130.6.a.h	4
130.6.b	\(\chi_{130}(79, \cdot)\)	130.6.b.a	12	1
		130.6.b.b	18
130.6.c	\(\chi_{130}(129, \cdot)\)	130.6.c.a	18	1
		130.6.c.b	18
130.6.d	\(\chi_{130}(51, \cdot)\)	130.6.d.a	12	1
		130.6.d.b	14
130.6.e	\(\chi_{130}(61, \cdot)\)	130.6.e.a	10	2
		130.6.e.b	10
		130.6.e.c	12
		130.6.e.d	12
130.6.g	\(\chi_{130}(57, \cdot)\)	130.6.g.a	34	2
		130.6.g.b	36
130.6.j	\(\chi_{130}(47, \cdot)\)	130.6.j.a	34	2
		130.6.j.b	36
130.6.l	\(\chi_{130}(101, \cdot)\)	130.6.l.a	20	2
		130.6.l.b	24
130.6.m	\(\chi_{130}(49, \cdot)\)	130.6.m.a	36	2
		130.6.m.b	36
130.6.n	\(\chi_{130}(9, \cdot)\)	130.6.n.a	68	2
130.6.p	\(\chi_{130}(7, \cdot)\)	n/a	140	4
130.6.s	\(\chi_{130}(33, \cdot)\)	n/a	140	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(130))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(130)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)