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

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