Space of modular forms of level 656, weight 4, and Character 656.o

• Label: 656.4.o
• Level: $656$
• Weight: $4$
• Character orbit: 656.o
• Rep. character: $\chi_{656}(245,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $500$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	656.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 656 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(656, [\chi])\).

	Total	New	Old
Modular forms	508	508	0
Cusp forms	500	500	0
Eisenstein series	8	8	0

Trace form

500 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 80 * q^8 + 8 * q^10 - 4 * q^16 + 28 * q^18 - 4 * q^20 - 112 * q^21 + 736 * q^31 - 624 * q^32 - 8 * q^33 - 1208 * q^36 - 4 * q^37 + 1556 * q^40 - 2868 * q^42 + 860 * q^43 + 604 * q^45 - 672 * q^46 + 23316 * q^49 + 1456 * q^50 + 104 * q^51 + 2036 * q^59 - 4 * q^61 - 528 * q^62 - 5500 * q^64 - 572 * q^66 - 268 * q^72 + 5872 * q^74 - 1376 * q^77 - 968 * q^78 + 2012 * q^80 - 37916 * q^81 - 1548 * q^82 - 4 * q^83 - 7048 * q^84 - 6748 * q^86 + 8960 * q^90 + 2224 * q^91 - 5360 * q^92 + 1376 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(656, [\chi])\) into newform subspaces

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