Space of modular forms of level 196, weight 10, and Character 196.f

• Label: 196.10.f
• Level: $196$
• Weight: $10$
• Character orbit: 196.f
• Rep. character: $\chi_{196}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $352$
• Sturm bound: $280$

Defining parameters

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	196.f (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(196, [\chi])\).

	Total	New	Old
Modular forms	520	368	152
Cusp forms	488	352	136
Eisenstein series	32	16	16

Trace form

352 * q - 33 * q^2 - 169 * q^4 + 6 * q^5 + 32394 * q^8 - 1102246 * q^9 + 26724 * q^10 - 82992 * q^12 - 14445 * q^16 + 6 * q^17 - 1625393 * q^18 - 1523132 * q^22 - 5971236 * q^24 + 62881278 * q^25 + 4366092 * q^26 - 1344248 * q^29 + 3806684 * q^30 + 24189967 * q^32 - 3850086 * q^33 + 90485298 * q^36 + 7285806 * q^37 + 2026692 * q^38 - 52452252 * q^40 - 7555270 * q^44 + 20589408 * q^45 + 95230374 * q^46 - 641585414 * q^50 - 72793296 * q^52 - 139471402 * q^53 + 519923844 * q^54 - 112527524 * q^57 + 217469918 * q^58 - 9796144 * q^60 - 165282894 * q^61 + 1740135146 * q^64 + 378864076 * q^65 + 809284128 * q^66 - 1273630140 * q^68 - 659736645 * q^72 - 998324670 * q^73 - 512143062 * q^74 - 3555593240 * q^78 - 1543676376 * q^80 - 6205150700 * q^81 + 1226449260 * q^82 + 377460748 * q^85 - 990501486 * q^86 + 68717366 * q^88 + 3866965866 * q^89 - 2159210332 * q^92 - 1476340794 * q^93 - 991145508 * q^94 + 769588536 * q^96

Decomposition of \(S_{10}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{10}^{\mathrm{old}}(196, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(196, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)