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

• Label: 700.6.w
• Level: $700$
• Weight: $6$
• Character orbit: 700.w
• Rep. character: $\chi_{700}(111,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $2384$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	700.w (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 700 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(720\)

Dimensions

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

	Total	New	Old
Modular forms	2416	2416	0
Cusp forms	2384	2384	0
Eisenstein series	32	32	0

Trace form

2384 * q - 6 * q^2 - 6 * q^4 + 732 * q^8 - 47640 * q^9 - 1281 * q^14 - 6 * q^16 + 1084 * q^18 - 1464 * q^21 - 134 * q^22 - 2744 * q^25 + 17531 * q^28 - 12 * q^29 - 24890 * q^30 + 4804 * q^32 - 18308 * q^36 - 12 * q^37 - 37001 * q^42 - 4102 * q^44 + 28226 * q^46 + 18376 * q^49 - 172592 * q^50 - 12 * q^53 + 58320 * q^56 + 43208 * q^57 + 212566 * q^58 - 36268 * q^60 - 205488 * q^64 - 24508 * q^65 - 199736 * q^70 + 483678 * q^72 - 24132 * q^74 - 19668 * q^77 + 563396 * q^78 - 3884208 * q^81 - 76824 * q^84 - 78100 * q^85 - 394 * q^86 - 942416 * q^88 + 515324 * q^92 - 4424 * q^93 + 229641 * 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.