Space of modular forms of level 196 and weight 8

• Label: 196.8
• Level: 196
• Weight: 8
• Dimension: 4558
• Nonzero newspaces: 8
• Sturm bound: 18816
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(18816\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(196))\).

	Total	New	Old
Modular forms	8382	4654	3728
Cusp forms	8082	4558	3524
Eisenstein series	300	96	204

Trace form

4558 * q - 15 * q^2 - 54 * q^3 - 15 * q^4 - 24 * q^5 - 21 * q^6 - 332 * q^7 + 1695 * q^8 + 10326 * q^9 - 19437 * q^10 - 20670 * q^11 + 27675 * q^12 + 62614 * q^13 + 19626 * q^14 - 31836 * q^15 - 95463 * q^16 + 19632 * q^17 - 51183 * q^18 - 22010 * q^19 - 21 * q^20 + 34617 * q^21 + 58941 * q^22 - 18642 * q^23 + 285267 * q^24 + 307562 * q^25 - 410253 * q^26 - 111420 * q^27 - 417306 * q^28 + 204402 * q^29 + 19059 * q^30 + 71722 * q^31 + 2696385 * q^32 - 1287780 * q^33 - 21 * q^34 - 906963 * q^35 - 5042337 * q^36 + 1356852 * q^37 - 808221 * q^38 + 4401975 * q^39 + 3744675 * q^40 + 2394900 * q^41 + 2942319 * q^42 - 903938 * q^43 - 3248337 * q^44 - 6568959 * q^45 - 6912825 * q^46 + 75540 * q^47 + 8061454 * q^49 + 5722242 * q^50 + 1409274 * q^51 + 6749547 * q^52 + 1113294 * q^53 - 10899741 * q^54 - 16663569 * q^55 - 3777510 * q^56 + 7139316 * q^57 + 9384135 * q^58 + 7156776 * q^59 + 6888843 * q^60 + 5992335 * q^61 - 21 * q^62 - 27456594 * q^63 - 5349273 * q^64 - 9200070 * q^65 - 3798405 * q^66 + 11074042 * q^67 + 6837747 * q^68 + 48285498 * q^69 + 399603 * q^70 + 26558784 * q^71 + 16354809 * q^72 - 13742672 * q^73 + 17002191 * q^74 - 76300104 * q^75 - 21 * q^76 - 36769635 * q^77 - 13441335 * q^78 - 5664146 * q^79 + 33908202 * q^80 + 71163036 * q^81 - 62807454 * q^82 + 9474228 * q^83 - 127339758 * q^84 + 62552562 * q^85 - 17151840 * q^86 + 38359932 * q^87 + 123218934 * q^88 - 73185876 * q^89 + 275149980 * q^90 - 2535028 * q^91 + 111648972 * q^92 - 45230568 * q^93 - 41126550 * q^94 - 7087590 * q^95 - 328243392 * q^96 + 10923988 * q^97 - 276486300 * q^98 + 66609648 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(196))\)

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
196.8.a	\(\chi_{196}(1, \cdot)\)	196.8.a.a	2	1
		196.8.a.b	2
		196.8.a.c	4
		196.8.a.d	5
		196.8.a.e	5
		196.8.a.f	6
196.8.d	\(\chi_{196}(195, \cdot)\)	n/a	136	1
196.8.e	\(\chi_{196}(165, \cdot)\)	196.8.e.a	4	2
		196.8.e.b	4
		196.8.e.c	4
		196.8.e.d	4
		196.8.e.e	8
		196.8.e.f	10
		196.8.e.g	12
196.8.f	\(\chi_{196}(19, \cdot)\)	n/a	272	2
196.8.i	\(\chi_{196}(29, \cdot)\)	n/a	192	6
196.8.j	\(\chi_{196}(27, \cdot)\)	n/a	1164	6
196.8.m	\(\chi_{196}(9, \cdot)\)	n/a	396	12
196.8.p	\(\chi_{196}(3, \cdot)\)	n/a	2328	12

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(196))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(196)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)