Space of modular forms of level 704, weight 5, and Character 704.bl

• Label: 704.5.bl
• Level: $704$
• Weight: $5$
• Character orbit: 704.bl
• Rep. character: $\chi_{704}(3,\cdot)$
• Character field: $\Q(\zeta_{80})$
• Dimension: $12224$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	704.bl (of order \(80\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 704 \)
Character field:			\(\Q(\zeta_{80})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(704, [\chi])\).

	Total	New	Old
Modular forms	12352	12352	0
Cusp forms	12224	12224	0
Eisenstein series	128	128	0

Trace form

12224 * q - 24 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 24 * q^6 - 24 * q^7 - 24 * q^8 - 24 * q^9 - 64 * q^10 - 32 * q^11 - 64 * q^12 - 24 * q^13 - 24 * q^14 - 24 * q^15 - 24 * q^16 - 24 * q^17 - 24 * q^18 - 24 * q^19 - 24 * q^20 - 64 * q^21 + 2632 * q^22 - 64 * q^23 - 24 * q^24 - 24 * q^25 + 16176 * q^26 - 24 * q^27 - 24 * q^28 - 24 * q^29 - 24 * q^30 - 48 * q^31 + 4976 * q^32 + 14096 * q^34 - 24 * q^35 - 24 * q^36 - 24 * q^37 - 24 * q^38 - 24 * q^39 - 744 * q^40 - 24 * q^41 - 24 * q^42 - 64 * q^43 - 8456 * q^44 - 64 * q^45 - 24 * q^46 - 24 * q^47 - 24 * q^48 - 24 * q^49 - 24 * q^50 - 24 * q^51 - 17976 * q^52 - 24 * q^53 - 64 * q^54 - 23584 * q^55 + 49328 * q^56 - 24 * q^57 - 24 * q^58 - 26136 * q^59 + 31944 * q^60 - 24 * q^61 + 232 * q^62 + 36552 * q^64 - 128 * q^65 - 35584 * q^66 + 75456 * q^67 - 24 * q^68 - 24 * q^69 - 61176 * q^70 + 39912 * q^71 - 24 * q^72 - 24 * q^73 - 33288 * q^74 - 13848 * q^75 - 64 * q^76 - 32 * q^77 + 99296 * q^78 - 24 * q^79 - 187224 * q^80 - 24 * q^81 - 24 * q^82 - 24 * q^83 - 115832 * q^84 - 24 * q^85 - 170376 * q^86 - 64 * q^87 - 71152 * q^88 - 64 * q^89 - 24 * q^90 - 24 * q^91 - 159624 * q^92 + 1272 * q^93 - 24 * q^94 - 48 * q^95 - 24 * q^96 - 64 * q^98 - 680 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(704, [\chi])\) into newform subspaces

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