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

• Label: 1764.4.ba
• Level: $1764$
• Weight: $4$
• Character orbit: 1764.ba
• Rep. character: $\chi_{1764}(491,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $1456$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1764.ba (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	2048	1496	552
Cusp forms	1984	1456	528
Eisenstein series	64	40	24

Trace form

1456 * q + 3 * q^2 + q^4 + 6 * q^5 + 9 * q^6 + 14 * q^9 + 20 * q^10 + 162 * q^12 + 2 * q^13 + q^16 - 218 * q^18 - 228 * q^20 - 21 * q^22 - 385 * q^24 + 17202 * q^25 - 114 * q^29 + 312 * q^30 - 687 * q^32 - 496 * q^33 - 205 * q^34 - 733 * q^36 + 8 * q^37 - 891 * q^38 - 214 * q^40 - 144 * q^41 - 678 * q^45 + 120 * q^46 - 281 * q^48 - 1239 * q^50 - 586 * q^52 + 1195 * q^54 - 678 * q^57 - 280 * q^58 - 264 * q^60 + 2 * q^61 + 394 * q^64 - 690 * q^65 + 4332 * q^66 - 243 * q^68 - 954 * q^69 - 3563 * q^72 - 820 * q^73 + 324 * q^74 - 621 * q^76 + 3810 * q^78 - 82 * q^81 + 722 * q^82 - 260 * q^85 + 8331 * q^86 + 1557 * q^88 - 4118 * q^90 - 756 * q^92 + 126 * q^93 + 138 * q^94 + 620 * q^96 + 20 * q^97

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

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

Decomposition of \(S_{4}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1764, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)