Space of modular forms of level 616, weight 4, and Character 616.bc

• Label: 616.4.bc
• Level: $616$
• Weight: $4$
• Character orbit: 616.bc
• Rep. character: $\chi_{616}(243,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $480$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	616.bc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(616, [\chi])\).

	Total	New	Old
Modular forms	584	480	104
Cusp forms	568	480	88
Eisenstein series	16	0	16

Trace form

480 * q - 84 * q^8 + 2160 * q^9 + 18 * q^10 - 330 * q^12 + 220 * q^14 - 28 * q^16 - 70 * q^18 - 6000 * q^25 + 750 * q^26 + 1372 * q^28 - 244 * q^30 - 880 * q^32 + 456 * q^35 + 1140 * q^36 - 2364 * q^38 + 2340 * q^40 - 1280 * q^42 + 308 * q^44 - 70 * q^46 - 720 * q^49 + 904 * q^50 + 1400 * q^51 - 2322 * q^52 + 3450 * q^54 - 978 * q^56 - 672 * q^57 - 1010 * q^58 + 2064 * q^59 + 2252 * q^60 - 2868 * q^64 + 1650 * q^66 - 1848 * q^67 - 1680 * q^68 + 3430 * q^70 - 1842 * q^72 - 1296 * q^73 - 1820 * q^74 + 6928 * q^78 + 6546 * q^80 - 20672 * q^81 - 930 * q^82 + 6196 * q^84 - 330 * q^86 - 396 * q^88 + 2544 * q^89 + 848 * q^91 + 3780 * q^92 - 4590 * q^94 + 17430 * q^96 + 4410 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(616, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(616, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(616, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)