Space of modular forms of level 627, weight 4, and Character 627.u

• Label: 627.4.u
• Level: $627$
• Weight: $4$
• Character orbit: 627.u
• Rep. character: $\chi_{627}(134,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $864$
• Sturm bound: $320$

Defining parameters

Level:	$N$	$=$	$627 = 3 \cdot 11 \cdot 19$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	627.u (of order $10$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$33$
Character field:			$\Q(\zeta_{10})$
Sturm bound:			$320$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(627, [\chi])$.

	Total	New	Old
Modular forms	976	864	112
Cusp forms	944	864	80
Eisenstein series	32	0	32

Trace form

864 * q - 4 * q^3 - 864 * q^4 + 64 * q^9 + 256 * q^12 - 180 * q^15 - 4152 * q^16 + 912 * q^22 + 6192 * q^25 + 260 * q^27 - 2400 * q^28 - 1692 * q^31 - 1432 * q^33 + 648 * q^34 - 1848 * q^36 + 1840 * q^39 + 1440 * q^40 + 1392 * q^42 + 4192 * q^45 - 720 * q^46 - 640 * q^48 + 9168 * q^49 - 1040 * q^51 + 4680 * q^52 - 120 * q^55 + 7512 * q^58 + 872 * q^60 - 420 * q^61 - 7900 * q^63 - 21912 * q^64 - 5802 * q^66 - 5664 * q^67 - 4420 * q^69 - 1032 * q^70 + 3270 * q^72 - 7560 * q^73 + 7096 * q^75 + 4212 * q^78 + 7080 * q^79 + 5976 * q^81 + 1224 * q^82 + 11360 * q^84 + 3360 * q^85 + 24024 * q^88 - 2600 * q^90 + 3768 * q^91 - 8292 * q^93 + 5400 * q^94 - 17580 * q^96 - 12120 * q^97 + 124 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(627, [\chi])$ into newform subspaces

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

Decomposition of $S_{4}^{\mathrm{old}}(627, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(627, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(33, [\chi])$$^{\oplus 2}$