Space of modular forms of level 600, weight 6, and Character 600.bm

• Label: 600.6.bm
• Level: $600$
• Weight: $6$
• Character orbit: 600.bm
• Rep. character: $\chi_{600}(61,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $1200$
• Sturm bound: $720$

Defining parameters

Level:	$N$	$=$	$600 = 2^{3} \cdot 3 \cdot 5^{2}$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	600.bm (of order $10$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$200$
Character field:			$\Q(\zeta_{10})$
Sturm bound:			$720$

Dimensions

The following table gives the dimensions of various subspaces of $M_{6}(600, [\chi])$.

	Total	New	Old
Modular forms	2416	1200	1216
Cusp forms	2384	1200	1184
Eisenstein series	32	0	32

Trace form

1200 * q + 738 * q^8 + 24300 * q^9 + 818 * q^10 + 792 * q^12 - 2748 * q^14 + 3828 * q^16 + 808 * q^17 + 2576 * q^20 + 3662 * q^22 + 3116 * q^25 + 12980 * q^26 + 17708 * q^28 - 6156 * q^30 - 23064 * q^31 + 25580 * q^32 + 12304 * q^34 - 78506 * q^38 + 24336 * q^39 - 46840 * q^40 + 4952 * q^41 - 14220 * q^42 - 31038 * q^44 - 14180 * q^46 - 130512 * q^47 + 44784 * q^48 + 2881200 * q^49 - 56304 * q^50 + 111536 * q^52 + 55024 * q^55 - 15804 * q^56 + 109006 * q^58 - 68922 * q^60 + 74154 * q^62 + 205482 * q^64 + 294564 * q^65 + 83448 * q^66 + 346256 * q^68 + 100684 * q^70 - 59778 * q^72 - 50360 * q^73 - 24244 * q^74 + 93608 * q^76 + 151416 * q^78 - 249640 * q^79 - 403856 * q^80 - 1968300 * q^81 - 705840 * q^82 - 23544 * q^84 - 94260 * q^86 - 182938 * q^88 + 526740 * q^89 + 150012 * q^90 - 115466 * q^92 - 2790 * q^94 + 780616 * q^95 - 81720 * q^96 + 359072 * q^97 - 689140 * q^98

Decomposition of $S_{6}^{\mathrm{new}}(600, [\chi])$ into newform subspaces

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

Decomposition of $S_{6}^{\mathrm{old}}(600, [\chi])$ into lower level spaces

$S_{6}^{\mathrm{old}}(600, [\chi]) \simeq$ $S_{6}^{\mathrm{new}}(200, [\chi])$$^{\oplus 2}$