Space of modular forms of level 700, weight 6, and Character 700.bq

• Label: 700.6.bq
• Level: $700$
• Weight: $6$
• Character orbit: 700.bq
• Rep. character: $\chi_{700}(31,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $4768$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	700.bq (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 700 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(700, [\chi])\).

	Total	New	Old
Modular forms	4832	4832	0
Cusp forms	4768	4768	0
Eisenstein series	64	64	0

Trace form

4768 * q - 3 * q^2 - 3 * q^4 - 24 * q^5 - 750 * q^8 + 47622 * q^9 + 789 * q^10 - 9 * q^12 + 1272 * q^14 - 3 * q^16 - 18 * q^17 + 350 * q^18 + 1446 * q^21 + 116 * q^22 - 1482 * q^24 - 1372 * q^25 - 216 * q^26 + 16108 * q^28 - 24 * q^29 - 1009 * q^30 - 4828 * q^32 + 28278 * q^33 - 51820 * q^36 - 6 * q^37 - 61866 * q^38 - 35067 * q^40 - 32992 * q^42 + 4093 * q^44 - 1482 * q^45 + 14305 * q^46 - 18424 * q^49 + 265238 * q^50 - 118014 * q^52 - 6 * q^53 - 46473 * q^54 + 92934 * q^56 + 80584 * q^57 - 66031 * q^58 + 166483 * q^60 - 18 * q^61 + 211158 * q^64 + 5734 * q^65 + 45189 * q^66 - 291810 * q^68 - 60067 * q^70 + 161256 * q^72 - 18 * q^73 - 12258 * q^74 + 19650 * q^77 - 202478 * q^78 - 954276 * q^80 + 3887106 * q^81 + 377124 * q^82 + 147447 * q^84 - 71252 * q^85 + 673 * q^86 + 44978 * q^88 - 18 * q^89 - 515342 * q^92 + 4376 * q^93 - 9 * q^94 + 446301 * q^96 + 943536 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(700, [\chi])\) into newform subspaces

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