Space of modular forms of level 1372, weight 4, and Character 1372.i

• Label: 1372.4.i
• Level: $1372$
• Weight: $4$
• Character orbit: 1372.i
• Rep. character: $\chi_{1372}(197,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $420$
• Sturm bound: $784$

Defining parameters

Level:	$N$	$=$	$1372 = 2^{2} \cdot 7^{3}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1372.i (of order $7$ and degree $6$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$49$
Character field:			$\Q(\zeta_{7})$
Sturm bound:			$784$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(1372, [\chi])$.

	Total	New	Old
Modular forms	3654	420	3234
Cusp forms	3402	420	2982
Eisenstein series	252	0	252

Trace form

420 * q - 6 * q^3 - 2 * q^5 - 700 * q^9 + 42 * q^11 - 94 * q^13 - 126 * q^15 + 136 * q^17 + 360 * q^19 - 238 * q^23 - 1946 * q^25 - 654 * q^27 + 182 * q^29 + 140 * q^31 + 352 * q^33 + 2450 * q^37 + 1610 * q^39 - 128 * q^41 - 28 * q^43 - 146 * q^45 - 344 * q^47 - 672 * q^51 + 952 * q^53 + 3440 * q^55 + 2772 * q^57 - 236 * q^59 - 1152 * q^61 + 812 * q^67 + 3324 * q^69 + 1778 * q^71 - 2052 * q^73 - 4366 * q^75 + 1372 * q^79 - 6748 * q^81 - 3434 * q^83 + 252 * q^85 - 2442 * q^87 + 2832 * q^89 + 8596 * q^93 + 4480 * q^95 + 568 * q^97 - 13048 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(1372, [\chi])$ into newform subspaces

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

Decomposition of $S_{4}^{\mathrm{old}}(1372, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(1372, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(49, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(98, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(196, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(343, [\chi])$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(686, [\chi])$$^{\oplus 2}$