Space of modular forms of level 197 and weight 10

• Label: 197.10
• Level: 197
• Weight: 10
• Dimension: 14455
• Nonzero newspaces: 6
• Sturm bound: 32340
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 197 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(32340\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(197))\).

	Total	New	Old
Modular forms	14651	14649	2
Cusp forms	14455	14455	0
Eisenstein series	196	194	2

Trace form

14455 * q - 98 * q^2 - 98 * q^3 - 98 * q^4 - 98 * q^5 - 98 * q^6 - 98 * q^7 - 98 * q^8 - 98 * q^9 - 98 * q^10 - 98 * q^11 - 98 * q^12 - 98 * q^13 - 98 * q^14 - 98 * q^15 - 98 * q^16 - 98 * q^17 - 98 * q^18 - 98 * q^19 - 98 * q^20 - 98 * q^21 - 98 * q^22 - 98 * q^23 - 98 * q^24 - 98 * q^25 - 98 * q^26 - 98 * q^27 - 98 * q^28 - 98 * q^29 - 98 * q^30 - 98 * q^31 - 98 * q^32 - 98 * q^33 - 98 * q^34 - 98 * q^35 - 98 * q^36 - 98 * q^37 - 98 * q^38 - 98 * q^39 - 98 * q^40 - 98 * q^41 - 98 * q^42 - 98 * q^43 - 98 * q^44 - 98 * q^45 - 98 * q^46 - 98 * q^47 - 98 * q^48 - 98 * q^49 - 98 * q^50 - 98 * q^51 - 98 * q^52 - 98 * q^53 - 98 * q^54 - 98 * q^55 - 98 * q^56 - 98 * q^57 - 98 * q^58 - 98 * q^59 - 98 * q^60 - 98 * q^61 - 98 * q^62 - 98 * q^63 - 98 * q^64 - 98 * q^65 - 98 * q^66 - 98 * q^67 - 98 * q^68 - 98 * q^69 - 98 * q^70 - 98 * q^71 - 98 * q^72 - 98 * q^73 - 98 * q^74 - 98 * q^75 - 98 * q^76 - 98 * q^77 - 98 * q^78 - 98 * q^79 - 98 * q^80 - 98 * q^81 - 98 * q^82 - 98 * q^83 - 98 * q^84 - 98 * q^85 - 98 * q^86 - 98 * q^87 - 98 * q^88 - 98 * q^89 - 98 * q^90 - 98 * q^91 - 98 * q^92 - 98 * q^93 - 98 * q^94 - 98 * q^95 - 98 * q^96 - 98 * q^97 - 98 * q^98 - 98 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(197))\)

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
197.10.a	\(\chi_{197}(1, \cdot)\)	197.10.a.a	71	1
		197.10.a.b	76
197.10.b	\(\chi_{197}(196, \cdot)\)	n/a	148	1
197.10.d	\(\chi_{197}(36, \cdot)\)	n/a	882	6
197.10.e	\(\chi_{197}(6, \cdot)\)	n/a	888	6
197.10.g	\(\chi_{197}(16, \cdot)\)	n/a	6174	42
197.10.h	\(\chi_{197}(4, \cdot)\)	n/a	6216	42

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