Space of modular forms of level 196 and weight 2

• Label: 196.2
• Level: 196
• Weight: 2
• Dimension: 610
• Nonzero newspaces: 8
• Newform subspaces: 16
• Sturm bound: 4704
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(4704\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(196))\).

	Total	New	Old
Modular forms	1326	706	620
Cusp forms	1027	610	417
Eisenstein series	299	96	203

Trace form

610 * q - 15 * q^2 + 2 * q^3 - 15 * q^4 - 24 * q^5 - 21 * q^6 + 4 * q^7 - 33 * q^8 - 34 * q^9 - 33 * q^10 - 6 * q^11 - 45 * q^12 - 50 * q^13 - 30 * q^14 - 12 * q^15 - 39 * q^16 - 24 * q^17 - 27 * q^18 - 2 * q^19 - 21 * q^20 - 47 * q^21 - 3 * q^22 + 6 * q^23 + 3 * q^24 - 46 * q^25 + 3 * q^26 + 20 * q^27 + 6 * q^28 - 78 * q^29 - 9 * q^30 - 14 * q^31 - 15 * q^32 - 60 * q^33 - 21 * q^34 - 15 * q^35 - 57 * q^36 - 84 * q^37 - 57 * q^38 - 45 * q^39 - 45 * q^40 - 108 * q^41 - 33 * q^42 - 26 * q^43 - 57 * q^44 - 159 * q^45 - 45 * q^46 - 60 * q^47 - 110 * q^49 - 66 * q^50 - 78 * q^51 - 21 * q^52 - 42 * q^53 + 15 * q^54 - 69 * q^55 - 30 * q^56 - 44 * q^57 - 9 * q^58 - 24 * q^59 + 3 * q^60 - 57 * q^61 - 21 * q^62 - 18 * q^63 - 57 * q^64 - 54 * q^65 - 9 * q^66 - 14 * q^67 - 21 * q^68 - 54 * q^69 - 27 * q^70 + 9 * q^72 - 104 * q^73 + 3 * q^74 + 8 * q^75 - 21 * q^76 - 63 * q^77 + 21 * q^78 - 26 * q^79 + 90 * q^80 - 28 * q^81 + 60 * q^82 + 36 * q^83 + 210 * q^84 - 54 * q^85 + 162 * q^86 + 156 * q^87 + 174 * q^88 - 36 * q^89 + 378 * q^90 + 92 * q^91 + 120 * q^92 + 184 * q^93 + 228 * q^94 + 162 * q^95 + 384 * q^96 + 124 * q^97 + 288 * q^98 + 144 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)

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
196.2.a	\(\chi_{196}(1, \cdot)\)	196.2.a.a	1	1
		196.2.a.b	1
		196.2.a.c	2
196.2.d	\(\chi_{196}(195, \cdot)\)	196.2.d.a	4	1
		196.2.d.b	4
		196.2.d.c	8
196.2.e	\(\chi_{196}(165, \cdot)\)	196.2.e.a	2	2
		196.2.e.b	4
196.2.f	\(\chi_{196}(19, \cdot)\)	196.2.f.a	4	2
		196.2.f.b	4
		196.2.f.c	8
		196.2.f.d	16
196.2.i	\(\chi_{196}(29, \cdot)\)	196.2.i.a	24	6
196.2.j	\(\chi_{196}(27, \cdot)\)	196.2.j.a	156	6
196.2.m	\(\chi_{196}(9, \cdot)\)	196.2.m.a	60	12
196.2.p	\(\chi_{196}(3, \cdot)\)	196.2.p.a	312	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(196))\) into lower level spaces

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