Space of modular forms of level 336, weight 4, and Character 336.bo

• Label: 336.4.bo
• Level: $336$
• Weight: $4$
• Character orbit: 336.bo
• Rep. character: $\chi_{336}(5,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $752$
• Sturm bound: $256$

Defining parameters

Level:	$N$	$=$	$336 = 2^{4} \cdot 3 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	336.bo (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$336$
Character field:			$\Q(\zeta_{12})$
Sturm bound:			$256$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(336, [\chi])$.

	Total	New	Old
Modular forms	784	784	0
Cusp forms	752	752	0
Eisenstein series	32	32	0

Trace form

752 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 + 236 * q^16 - 40 * q^18 - 12 * q^19 + 50 * q^21 + 488 * q^22 - 6 * q^24 - 300 * q^28 - 566 * q^30 - 24 * q^31 - 12 * q^33 + 176 * q^36 - 4 * q^37 - 2352 * q^40 - 1998 * q^42 - 16 * q^43 - 6 * q^45 + 60 * q^46 - 16 * q^49 + 806 * q^51 - 2496 * q^52 + 4446 * q^54 - 772 * q^58 + 2070 * q^60 - 12 * q^61 - 1380 * q^63 - 3040 * q^64 - 3306 * q^66 + 1628 * q^67 + 7988 * q^70 + 962 * q^72 + 744 * q^75 + 5876 * q^78 - 8 * q^79 - 4 * q^81 + 5304 * q^82 - 6336 * q^84 + 984 * q^85 + 3212 * q^88 - 952 * q^91 - 110 * q^93 + 7008 * q^94 - 9696 * q^96 + 2908 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(336, [\chi])$ into newform subspaces

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