Space of modular forms of level 1710, weight 2, and Character 1710.dh

• Label: 1710.2.dh
• Level: $1710$
• Weight: $2$
• Character orbit: 1710.dh
• Rep. character: $\chi_{1710}(47,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $1440$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.dh (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 855 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1710, [\chi])\).

	Total	New	Old
Modular forms	4416	1440	2976
Cusp forms	4224	1440	2784
Eisenstein series	192	0	192

Trace form

\( 1440 q + 72 q^{15} + 108 q^{17} + 24 q^{18} + 72 q^{23} - 36 q^{33} + 72 q^{45} + 24 q^{51} - 216 q^{57} + 24 q^{60} - 36 q^{63} - 24 q^{66} - 48 q^{78} - 96 q^{87} + 12 q^{90} + 60 q^{93} + 216 q^{98}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1710, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1710, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 2}\)