Space of modular forms of level 197 and weight 2

• Label: 197.2
• Level: 197
• Weight: 2
• Dimension: 1520
• Nonzero newspaces: 6
• Newform subspaces: 9
• Sturm bound: 6468
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 197 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(6468\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(197))\).

	Total	New	Old
Modular forms	1715	1715	0
Cusp forms	1520	1520	0
Eisenstein series	195	195	0

Trace form

1520 * q - 95 * q^2 - 94 * q^3 - 91 * q^4 - 92 * q^5 - 86 * q^6 - 90 * q^7 - 83 * q^8 - 85 * q^9 - 80 * q^10 - 86 * q^11 - 70 * q^12 - 84 * q^13 - 74 * q^14 - 74 * q^15 - 67 * q^16 - 80 * q^17 - 59 * q^18 - 78 * q^19 - 56 * q^20 - 66 * q^21 - 62 * q^22 - 74 * q^23 - 38 * q^24 - 67 * q^25 - 56 * q^26 - 58 * q^27 - 42 * q^28 - 68 * q^29 - 26 * q^30 - 66 * q^31 - 35 * q^32 - 50 * q^33 - 44 * q^34 - 50 * q^35 - 7 * q^36 - 60 * q^37 - 38 * q^38 - 42 * q^39 - 8 * q^40 - 56 * q^41 - 2 * q^42 - 54 * q^43 - 14 * q^44 - 20 * q^45 - 26 * q^46 - 50 * q^47 + 26 * q^48 - 41 * q^49 - 5 * q^50 - 26 * q^51 - 44 * q^53 + 22 * q^54 - 26 * q^55 + 22 * q^56 - 18 * q^57 - 8 * q^58 - 38 * q^59 + 70 * q^60 - 36 * q^61 - 2 * q^62 + 6 * q^63 + 29 * q^64 - 14 * q^65 + 46 * q^66 - 30 * q^67 + 28 * q^68 - 2 * q^69 + 46 * q^70 - 26 * q^71 + 97 * q^72 - 24 * q^73 + 16 * q^74 + 26 * q^75 + 42 * q^76 - 2 * q^77 + 70 * q^78 - 18 * q^79 + 88 * q^80 + 23 * q^81 + 28 * q^82 - 14 * q^83 + 126 * q^84 + 10 * q^85 + 34 * q^86 + 22 * q^87 + 82 * q^88 - 8 * q^89 + 136 * q^90 + 14 * q^91 + 70 * q^92 + 30 * q^93 + 46 * q^94 + 22 * q^95 + 154 * q^96 + 73 * q^98 + 58 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(197))\)

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
197.2.a	\(\chi_{197}(1, \cdot)\)	197.2.a.a	1	1
		197.2.a.b	5
		197.2.a.c	10
197.2.b	\(\chi_{197}(196, \cdot)\)	197.2.b.a	16	1
197.2.d	\(\chi_{197}(36, \cdot)\)	197.2.d.a	90	6
197.2.e	\(\chi_{197}(6, \cdot)\)	197.2.e.a	6	6
		197.2.e.b	90
197.2.g	\(\chi_{197}(16, \cdot)\)	197.2.g.a	630	42
197.2.h	\(\chi_{197}(4, \cdot)\)	197.2.h.a	672	42