Space of modular forms of level 196, weight 5, and Character 196.o

• Label: 196.5.o
• Level: $196$
• Weight: $5$
• Character orbit: 196.o
• Rep. character: $\chi_{196}(11,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1320$
• Sturm bound: $140$

Defining parameters

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	196.o (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 196 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(140\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(196, [\chi])\).

	Total	New	Old
Modular forms	1368	1368	0
Cusp forms	1320	1320	0
Eisenstein series	48	48	0

Trace form

1320 * q - 13 * q^2 - 13 * q^4 - 26 * q^5 + 22 * q^6 + 80 * q^8 - 2888 * q^9 - 144 * q^10 - 771 * q^12 - 372 * q^13 - 1535 * q^14 + 263 * q^16 - 26 * q^17 + 156 * q^18 - 678 * q^20 - 454 * q^21 - 494 * q^22 + 5592 * q^24 + 12356 * q^25 + 426 * q^26 - 7596 * q^28 - 2660 * q^29 - 459 * q^30 - 223 * q^32 + 1018 * q^33 + 3026 * q^34 + 1060 * q^36 - 8346 * q^37 + 1272 * q^38 + 8502 * q^40 + 1228 * q^41 - 3610 * q^42 - 8510 * q^44 - 3088 * q^45 + 3864 * q^46 + 23268 * q^48 + 5128 * q^49 + 14768 * q^50 - 6014 * q^52 + 790 * q^53 + 7481 * q^54 - 17096 * q^56 - 12062 * q^57 - 1804 * q^58 - 58310 * q^60 + 18630 * q^61 - 34434 * q^62 + 5372 * q^64 + 24 * q^65 - 56200 * q^66 - 15059 * q^68 + 24016 * q^69 - 9778 * q^70 + 55628 * q^72 + 54 * q^73 + 15162 * q^74 - 5361 * q^76 - 12310 * q^77 - 21392 * q^78 - 45356 * q^80 + 17778 * q^81 - 38566 * q^82 - 19460 * q^84 + 16776 * q^85 + 33067 * q^86 + 105589 * q^88 + 19030 * q^89 + 103972 * q^90 - 34574 * q^92 - 3892 * q^93 - 14678 * q^94 + 123314 * q^96 + 13808 * q^97 + 37283 * q^98

Decomposition of \(S_{5}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

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