Space of modular forms of level 2380, weight 2, and Character 2380.dz

• Label: 2380.2.dz
• Level: $2380$
• Weight: $2$
• Character orbit: 2380.dz
• Rep. character: $\chi_{2380}(71,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $1728$
• Sturm bound: $864$

Defining parameters

Level:	$N$	$=$	$2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	2380.dz (of order $16$ and degree $8$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$68$
Character field:			$\Q(\zeta_{16})$
Sturm bound:			$864$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(2380, [\chi])$.

	Total	New	Old
Modular forms	3520	1728	1792
Cusp forms	3392	1728	1664
Eisenstein series	128	0	128

Trace form

$1728 q + 32 q^{24} + 160 q^{32} + 128 q^{34} + 128 q^{36} + 160 q^{38} + 32 q^{46} + 320 q^{57} - 192 q^{64} - 416 q^{66} - 416 q^{72} - 192 q^{74} + 320 q^{81} + 256 q^{88} + 224 q^{92}+O(q^{100})$

Decomposition of $S_{2}^{\mathrm{new}}(2380, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(2380, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(2380, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(68, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(340, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(476, [\chi])$$^{\oplus 2}$