Space of modular forms of level 1764, weight 4, and Character 1764.cz

• Label: 1764.4.cz
• Level: $1764$
• Weight: $4$
• Character orbit: 1764.cz
• Rep. character: $\chi_{1764}(95,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $12048$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1764.cz (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1764 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1764, [\chi])\).

	Total	New	Old
Modular forms	12144	12144	0
Cusp forms	12048	12048	0
Eisenstein series	96	96	0

Trace form

12048 * q - 18 * q^2 - 8 * q^4 - 42 * q^5 - 2 * q^6 - 26 * q^9 - 42 * q^10 - 234 * q^12 - 10 * q^13 - 18 * q^14 - 8 * q^16 - 60 * q^18 - 15 * q^20 - 268 * q^21 + 11 * q^22 + 264 * q^24 + 49390 * q^25 + 24 * q^26 - 88 * q^28 - 534 * q^29 - 93 * q^30 - 18 * q^32 + 190 * q^33 + 3 * q^34 + 754 * q^36 - 52 * q^37 - 21 * q^38 - 255 * q^40 - 30 * q^41 + 299 * q^42 - 771 * q^44 - 1246 * q^45 - 10 * q^46 - 537 * q^48 - 12 * q^49 - 411 * q^50 - 261 * q^52 - 82 * q^54 - 963 * q^56 - 290 * q^57 + 27 * q^58 - 6728 * q^60 - 16 * q^61 - 168 * q^62 - 20 * q^64 - 36 * q^65 - 97 * q^66 - 1550 * q^69 - 865 * q^70 - 1603 * q^72 - 52 * q^73 - 21 * q^74 + 507 * q^76 - 1020 * q^77 - 6305 * q^78 + 3297 * q^80 - 20046 * q^81 - 18 * q^82 - 13121 * q^84 + 240 * q^85 - 21 * q^86 + 1019 * q^88 + 3180 * q^89 - 7541 * q^90 + 23925 * q^92 - 184 * q^93 - 40 * q^94 - 10801 * q^96 - 24 * q^97 - 4515 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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