Space of modular forms of level 704, weight 6, and Character 704.bb

• Label: 704.6.bb
• Level: $704$
• Weight: $6$
• Character orbit: 704.bb
• Rep. character: $\chi_{704}(43,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $3824$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	704.bb (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 704 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(704, [\chi])\).

	Total	New	Old
Modular forms	3856	3856	0
Cusp forms	3824	3824	0
Eisenstein series	32	32	0

Trace form

3824 * q - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^9 - 8 * q^11 - 16 * q^12 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^20 - 13600 * q^22 - 16 * q^23 - 16 * q^25 + 51904 * q^26 - 16 * q^27 - 32 * q^31 + 25504 * q^34 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^42 - 65520 * q^44 - 16 * q^45 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 16 * q^53 - 220104 * q^55 - 301856 * q^56 - 16 * q^58 + 57904 * q^59 - 197872 * q^60 + 749744 * q^64 - 255144 * q^66 - 244656 * q^67 - 16 * q^69 + 286928 * q^70 - 287696 * q^71 + 772976 * q^75 - 8 * q^77 + 389648 * q^78 - 387216 * q^80 - 16 * q^81 - 16 * q^82 + 1443712 * q^86 - 223288 * q^88 - 16 * q^89 - 16 * q^91 + 1842528 * q^92 - 3904 * q^93 + 1936 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(704, [\chi])\) into newform subspaces

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