Space of modular forms of level 676 and weight 6

• Label: 676.6
• Level: 676
• Weight: 6
• Dimension: 40712
• Nonzero newspaces: 12
• Sturm bound: 170352
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(170352\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(676))\).

	Total	New	Old
Modular forms	71550	41120	30430
Cusp forms	70410	40712	29698
Eisenstein series	1140	408	732

Trace form

40712 * q - 66 * q^2 - 12 * q^3 - 66 * q^4 - 78 * q^5 - 66 * q^6 + 508 * q^7 - 66 * q^8 - 1527 * q^9 - 66 * q^10 + 1608 * q^11 - 78 * q^12 + 1428 * q^13 - 126 * q^14 - 3024 * q^15 - 66 * q^16 - 10596 * q^17 - 2910 * q^18 + 9820 * q^19 + 22734 * q^20 + 23448 * q^21 + 1674 * q^22 - 10560 * q^23 - 48546 * q^24 - 19115 * q^25 - 18042 * q^26 - 26208 * q^27 - 6606 * q^28 + 16644 * q^29 + 69534 * q^30 - 3020 * q^31 + 76674 * q^32 + 21240 * q^33 + 26094 * q^34 - 492 * q^35 - 100434 * q^36 - 1904 * q^37 - 78 * q^38 + 12084 * q^39 + 82482 * q^40 + 89388 * q^41 - 138414 * q^42 + 40824 * q^43 - 127926 * q^44 + 1692 * q^45 - 85146 * q^46 - 101748 * q^47 + 104478 * q^48 - 308063 * q^49 + 253458 * q^50 + 122664 * q^51 + 137574 * q^52 - 181302 * q^53 + 165762 * q^54 - 137652 * q^55 - 47478 * q^56 + 70968 * q^57 - 265122 * q^58 + 70872 * q^59 - 567846 * q^60 + 428960 * q^61 - 695610 * q^62 + 150300 * q^63 - 78 * q^64 + 62991 * q^65 + 1095882 * q^66 + 275116 * q^67 + 832818 * q^68 + 382992 * q^69 + 467850 * q^70 + 9024 * q^71 - 63870 * q^72 - 240674 * q^73 - 597978 * q^74 - 826452 * q^75 - 665946 * q^76 - 944388 * q^77 - 667086 * q^78 - 620920 * q^79 - 985254 * q^80 - 176991 * q^81 - 143946 * q^82 + 56400 * q^83 + 687306 * q^84 + 795534 * q^85 + 1867770 * q^86 + 1207776 * q^87 + 1314570 * q^88 + 958134 * q^89 - 78 * q^90 + 371698 * q^91 - 379758 * q^92 - 370656 * q^93 - 1496634 * q^94 - 873384 * q^95 - 1819470 * q^96 + 261502 * q^97 + 109182 * q^98 - 337896 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(676))\)

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
676.6.a	\(\chi_{676}(1, \cdot)\)	676.6.a.a	1	1
		676.6.a.b	1
		676.6.a.c	1
		676.6.a.d	3
		676.6.a.e	6
		676.6.a.f	6
		676.6.a.g	6
		676.6.a.h	10
		676.6.a.i	15
		676.6.a.j	15
676.6.d	\(\chi_{676}(337, \cdot)\)	676.6.d.a	2	1
		676.6.d.b	2
		676.6.d.c	2
		676.6.d.d	6
		676.6.d.e	10
		676.6.d.f	12
		676.6.d.g	30
676.6.e	\(\chi_{676}(529, \cdot)\)	n/a	128	2
676.6.f	\(\chi_{676}(99, \cdot)\)	n/a	750	2
676.6.h	\(\chi_{676}(361, \cdot)\)	n/a	130	2
676.6.l	\(\chi_{676}(19, \cdot)\)	n/a	1500	4
676.6.m	\(\chi_{676}(53, \cdot)\)	n/a	924	12
676.6.n	\(\chi_{676}(25, \cdot)\)	n/a	912	12
676.6.q	\(\chi_{676}(9, \cdot)\)	n/a	1824	24
676.6.s	\(\chi_{676}(31, \cdot)\)	n/a	10872	24
676.6.v	\(\chi_{676}(17, \cdot)\)	n/a	1800	24
676.6.w	\(\chi_{676}(7, \cdot)\)	n/a	21744	48

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(676))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(676)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)