Space of modular forms of level 440, weight 4, and Character 440.g

• Label: 440.4.g
• Level: $440$
• Weight: $4$
• Character orbit: 440.g
• Rep. character: $\chi_{440}(221,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Sturm bound: $288$

Defining parameters

Level:	$N$	$=$	$440 = 2^{3} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	440.g (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$8$
Character field:			$\Q$
Sturm bound:			$288$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(440, [\chi])$.

	Total	New	Old
Modular forms	220	120	100
Cusp forms	212	120	92
Eisenstein series	8	0	8

Trace form

120 * q - 12 * q^4 + 72 * q^6 + 12 * q^8 - 1080 * q^9 - 60 * q^10 - 376 * q^12 - 48 * q^14 + 120 * q^15 - 160 * q^16 + 232 * q^18 - 20 * q^20 - 552 * q^23 - 728 * q^24 - 3000 * q^25 + 252 * q^26 + 380 * q^28 + 528 * q^31 - 1120 * q^32 - 688 * q^34 - 1288 * q^36 - 800 * q^38 - 1200 * q^39 - 240 * q^40 - 1240 * q^42 - 308 * q^44 - 256 * q^46 + 1880 * q^47 + 1432 * q^48 + 4440 * q^49 - 1836 * q^52 + 248 * q^54 - 440 * q^55 + 2792 * q^56 + 672 * q^57 + 2560 * q^58 + 660 * q^60 - 1528 * q^62 + 80 * q^63 + 132 * q^64 - 1100 * q^66 + 1620 * q^68 - 620 * q^70 + 112 * q^71 + 3652 * q^72 - 864 * q^73 + 1872 * q^74 + 576 * q^76 - 3680 * q^78 - 2832 * q^79 - 880 * q^80 + 8488 * q^81 + 1432 * q^82 - 848 * q^84 - 2012 * q^86 + 8112 * q^87 + 848 * q^89 + 4500 * q^90 - 1928 * q^92 + 1288 * q^94 + 10984 * q^96 + 3168 * q^97 + 10512 * q^98

Decomposition of $S_{4}^{\mathrm{new}}(440, [\chi])$ into newform subspaces

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

Decomposition of $S_{4}^{\mathrm{old}}(440, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(440, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(8, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(40, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(88, [\chi])$$^{\oplus 2}$