Space of modular forms of level 1764, weight 2, and Character 1764.cz

• Label: 1764.2.cz
• Level: $1764$
• Weight: $2$
• Character orbit: 1764.cz
• Rep. character: $\chi_{1764}(95,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $3984$
• Sturm bound: $672$

Defining parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.cz (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1764 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1764, [\chi])\).

	Total	New	Old
Modular forms	4080	4080	0
Cusp forms	3984	3984	0
Eisenstein series	96	96	0

Trace form

3984 * q - 18 * q^2 - 8 * q^4 - 42 * q^5 - 8 * q^6 - 26 * q^9 - 30 * q^10 + 18 * q^12 - 10 * q^13 - 18 * q^14 - 8 * q^16 - 12 * q^18 - 15 * q^20 - 28 * q^21 - q^22 + 622 * q^25 + 6 * q^26 - 28 * q^28 - 102 * q^29 - 9 * q^30 - 18 * q^32 - 2 * q^33 - 3 * q^34 - 26 * q^36 - 52 * q^37 - 21 * q^38 - 15 * q^40 - 30 * q^41 - q^42 + 57 * q^44 - 70 * q^45 - 22 * q^46 + 15 * q^48 - 12 * q^49 - 51 * q^50 - 21 * q^52 + 8 * q^54 + 45 * q^56 - 50 * q^57 + 3 * q^58 + 160 * q^60 - 16 * q^61 - 42 * q^62 - 20 * q^64 - 36 * q^65 - 187 * q^66 + 34 * q^69 - 37 * q^70 - 43 * q^72 - 52 * q^73 - 21 * q^74 + 27 * q^76 - 12 * q^77 - 125 * q^78 - 87 * q^80 + 234 * q^81 - 24 * q^82 - 161 * q^84 - 21 * q^86 + 11 * q^88 - 60 * q^89 + 43 * q^90 + 165 * q^92 - 40 * q^93 - 16 * q^94 - q^96 - 24 * q^97 + 57 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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