Space of modular forms of level 1312, weight 4, and Character 1312.l

• Label: 1312.4.l
• Level: $1312$
• Weight: $4$
• Character orbit: 1312.l
• Rep. character: $\chi_{1312}(993,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $252$
• Sturm bound: $672$

Defining parameters

Level:	$N$	$=$	$1312 = 2^{5} \cdot 41$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1312.l (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$41$
Character field:			$\Q(i)$
Sturm bound:			$672$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(1312, [\chi])$.

	Total	New	Old
Modular forms	1024	252	772
Cusp forms	992	252	740
Eisenstein series	32	0	32

Trace form

$252 q + 92 q^{13} - 308 q^{17} - 6564 q^{25} - 172 q^{29} + 116 q^{41} + 360 q^{45} - 572 q^{53} - 2064 q^{57} - 1400 q^{65} + 2032 q^{69} - 22284 q^{81} + 5768 q^{85} + 2244 q^{89} - 1824 q^{93} + 2796 q^{97}+O(q^{100})$

Decomposition of $S_{4}^{\mathrm{new}}(1312, [\chi])$ into newform subspaces

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

Decomposition of $S_{4}^{\mathrm{old}}(1312, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(1312, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(41, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(82, [\chi])$$^{\oplus 5}$$\oplus$$S_{4}^{\mathrm{new}}(164, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(328, [\chi])$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(656, [\chi])$$^{\oplus 2}$