Space of modular forms of level 196 and weight 6

• Label: 196.6
• Level: 196
• Weight: 6
• Dimension: 3243
• Nonzero newspaces: 8
• Sturm bound: 14112
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(14112\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(196))\).

	Total	New	Old
Modular forms	6030	3339	2691
Cusp forms	5730	3243	2487
Eisenstein series	300	96	204

Trace form

3243 * q - 15 * q^2 + 6 * q^3 - 15 * q^4 + 90 * q^5 - 21 * q^6 + 116 * q^7 - 561 * q^8 + 363 * q^9 + 1587 * q^10 + 6 * q^11 - 3285 * q^12 + 148 * q^13 - 1878 * q^14 - 5412 * q^15 + 2265 * q^16 + 2214 * q^17 + 13473 * q^18 + 6610 * q^19 - 21 * q^20 + 7779 * q^21 - 26451 * q^22 - 474 * q^23 - 1149 * q^24 - 14599 * q^25 + 17763 * q^26 - 37764 * q^27 + 16806 * q^28 - 29328 * q^29 - 10749 * q^30 - 182 * q^31 - 16815 * q^32 + 93288 * q^33 - 21 * q^34 + 41145 * q^35 + 19983 * q^36 - 47698 * q^37 + 11283 * q^38 - 29649 * q^39 - 70125 * q^40 - 28494 * q^41 - 30777 * q^42 - 58430 * q^43 - 40209 * q^44 - 92667 * q^45 - 32505 * q^46 + 34836 * q^47 - 112558 * q^49 + 159042 * q^50 - 11142 * q^51 + 123531 * q^52 - 58884 * q^53 + 61971 * q^54 - 69609 * q^55 - 27750 * q^56 + 114144 * q^57 + 225447 * q^58 + 251508 * q^59 + 237339 * q^60 + 210215 * q^61 - 21 * q^62 - 168018 * q^63 - 199929 * q^64 - 150378 * q^65 - 443637 * q^66 - 290570 * q^67 - 50061 * q^68 - 420702 * q^69 - 160509 * q^70 - 157752 * q^71 - 518823 * q^72 + 384190 * q^73 - 535761 * q^74 + 450372 * q^75 - 21 * q^76 + 176463 * q^77 + 573033 * q^78 + 263854 * q^79 + 1849770 * q^80 - 9063 * q^81 + 993546 * q^82 - 411048 * q^83 - 1036350 * q^84 - 1022514 * q^85 - 799992 * q^86 - 1292124 * q^87 - 1237290 * q^88 - 188238 * q^89 - 1088892 * q^90 + 23164 * q^91 - 256164 * q^92 + 1808628 * q^93 + 485634 * q^94 + 1318722 * q^95 + 1064160 * q^96 + 339502 * q^97 + 1909020 * q^98 + 846396 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(196))\)

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
196.6.a	\(\chi_{196}(1, \cdot)\)	196.6.a.a	1	1
		196.6.a.b	1
		196.6.a.c	1
		196.6.a.d	1
		196.6.a.e	1
		196.6.a.f	1
		196.6.a.g	1
		196.6.a.h	2
		196.6.a.i	2
		196.6.a.j	2
		196.6.a.k	4
196.6.d	\(\chi_{196}(195, \cdot)\)	196.6.d.a	4	1
		196.6.d.b	36
		196.6.d.c	56
196.6.e	\(\chi_{196}(165, \cdot)\)	196.6.e.a	2	2
		196.6.e.b	2
		196.6.e.c	2
		196.6.e.d	2
		196.6.e.e	2
		196.6.e.f	2
		196.6.e.g	2
		196.6.e.h	2
		196.6.e.i	2
		196.6.e.j	4
		196.6.e.k	4
		196.6.e.l	8
196.6.f	\(\chi_{196}(19, \cdot)\)	n/a	192	2
196.6.i	\(\chi_{196}(29, \cdot)\)	n/a	144	6
196.6.j	\(\chi_{196}(27, \cdot)\)	n/a	828	6
196.6.m	\(\chi_{196}(9, \cdot)\)	n/a	276	12
196.6.p	\(\chi_{196}(3, \cdot)\)	n/a	1656	12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(196))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(196)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)