Space of modular forms of level 196 and weight 5

• Label: 196.5
• Level: 196
• Weight: 5
• Dimension: 2585
• Nonzero newspaces: 8
• Sturm bound: 11760
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(11760\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(196))\).

	Total	New	Old
Modular forms	4854	2683	2171
Cusp forms	4554	2585	1969
Eisenstein series	300	98	202

Trace form

2585 * q - 19 * q^2 - 18 * q^3 + q^4 + 10 * q^5 - 9 * q^6 - 52 * q^7 + 179 * q^8 - 261 * q^9 - 553 * q^10 - 342 * q^11 - 705 * q^12 - 256 * q^13 + 306 * q^14 + 1548 * q^15 + 1897 * q^16 + 2506 * q^17 + 825 * q^18 + 1494 * q^19 - 2501 * q^20 - 1965 * q^21 + 825 * q^22 - 3438 * q^23 + 3711 * q^24 - 7195 * q^25 + 2563 * q^26 - 1338 * q^28 + 9676 * q^29 - 3705 * q^30 + 10710 * q^31 - 2299 * q^32 + 8016 * q^33 - 10873 * q^34 - 4005 * q^35 - 10401 * q^36 - 3886 * q^37 - 3165 * q^38 - 15501 * q^39 - 109 * q^40 - 12758 * q^41 - 1167 * q^42 - 874 * q^43 + 6915 * q^44 - 1215 * q^45 + 23055 * q^46 + 15588 * q^47 + 39450 * q^48 + 8752 * q^49 + 27678 * q^50 + 13698 * q^51 + 6371 * q^52 + 12856 * q^53 - 7137 * q^54 + 44835 * q^55 - 660 * q^56 + 18144 * q^57 - 11089 * q^58 + 4500 * q^59 - 62997 * q^60 - 57393 * q^61 - 56709 * q^62 - 56256 * q^63 - 50777 * q^64 - 22678 * q^65 - 42105 * q^66 - 13118 * q^67 - 30953 * q^68 + 38958 * q^69 + 12489 * q^70 + 8064 * q^71 + 72525 * q^72 - 14302 * q^73 + 82579 * q^74 + 6876 * q^75 + 103815 * q^76 - 6111 * q^77 + 95817 * q^78 + 31474 * q^79 - 27476 * q^80 - 132543 * q^81 - 48556 * q^82 - 35280 * q^83 - 32130 * q^84 + 4426 * q^85 - 41754 * q^86 + 44292 * q^87 + 62124 * q^88 + 139090 * q^89 + 145782 * q^90 + 81768 * q^91 - 52758 * q^92 + 182352 * q^93 - 42396 * q^94 + 111294 * q^95 - 6126 * q^96 - 6010 * q^97 - 27432 * q^98 - 83760 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(196))\)

We only show spaces with odd 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
196.5.b	\(\chi_{196}(97, \cdot)\)	196.5.b.a	6	1
		196.5.b.b	8
196.5.c	\(\chi_{196}(99, \cdot)\)	196.5.c.a	1	1
		196.5.c.b	1
		196.5.c.c	1
		196.5.c.d	2
		196.5.c.e	8
		196.5.c.f	12
		196.5.c.g	14
		196.5.c.h	14
		196.5.c.i	24
196.5.g	\(\chi_{196}(67, \cdot)\)	n/a	152	2
196.5.h	\(\chi_{196}(117, \cdot)\)	196.5.h.a	2	2
		196.5.h.b	2
		196.5.h.c	6
		196.5.h.d	16
196.5.k	\(\chi_{196}(15, \cdot)\)	n/a	660	6
196.5.l	\(\chi_{196}(13, \cdot)\)	n/a	108	6
196.5.n	\(\chi_{196}(5, \cdot)\)	n/a	228	12
196.5.o	\(\chi_{196}(11, \cdot)\)	n/a	1320	12

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(196))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(196)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)