Space of modular forms of level 400, weight 6, and Character 400.y

• Label: 400.6.y
• Level: $400$
• Weight: $6$
• Character orbit: 400.y
• Rep. character: $\chi_{400}(129,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $296$
• Sturm bound: $360$

Defining parameters

Level:	$N$	$=$	$400 = 2^{4} \cdot 5^{2}$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	400.y (of order $10$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$25$
Character field:			$\Q(\zeta_{10})$
Sturm bound:			$360$

Dimensions

The following table gives the dimensions of various subspaces of $M_{6}(400, [\chi])$.

	Total	New	Old
Modular forms	1224	304	920
Cusp forms	1176	296	880
Eisenstein series	48	8	40

Trace form

296 * q + 5 * q^3 - 23 * q^5 + 5829 * q^9 - 723 * q^11 - 5 * q^13 - 1187 * q^15 - 5 * q^17 + 2169 * q^19 + 726 * q^21 - 9565 * q^23 + 581 * q^25 + 5 * q^27 - 4285 * q^29 + 5769 * q^31 - 5 * q^33 - 2908 * q^35 - 23530 * q^37 - 11679 * q^39 + 1235 * q^41 + 10573 * q^45 + 5 * q^47 - 634688 * q^49 + 125342 * q^51 - 50310 * q^53 - 22947 * q^55 + 62661 * q^59 - 45793 * q^61 - 84030 * q^63 + 82504 * q^65 + 111575 * q^67 - 489 * q^69 + 70577 * q^71 - 5 * q^73 + 85589 * q^75 + 84030 * q^77 - 62407 * q^79 - 247779 * q^81 - 260425 * q^83 - 10560 * q^85 + 556745 * q^87 + 131682 * q^89 - 149790 * q^91 + 168447 * q^95 - 165225 * q^97 - 823276 * q^99

Decomposition of $S_{6}^{\mathrm{new}}(400, [\chi])$ into newform subspaces

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

Decomposition of $S_{6}^{\mathrm{old}}(400, [\chi])$ into lower level spaces

$S_{6}^{\mathrm{old}}(400, [\chi]) \simeq$ $S_{6}^{\mathrm{new}}(25, [\chi])$$^{\oplus 5}$$\oplus$$S_{6}^{\mathrm{new}}(50, [\chi])$$^{\oplus 4}$$\oplus$$S_{6}^{\mathrm{new}}(100, [\chi])$$^{\oplus 3}$$\oplus$$S_{6}^{\mathrm{new}}(200, [\chi])$$^{\oplus 2}$