Space of modular forms of level 1530, weight 2, and Character 1530.cn

• Label: 1530.2.cn
• Level: $1530$
• Weight: $2$
• Character orbit: 1530.cn
• Rep. character: $\chi_{1530}(97,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $1728$
• Sturm bound: $648$

Defining parameters

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.cn (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 765 \)
Character field:			\(\Q(\zeta_{48})\)
Sturm bound:			\(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1530, [\chi])\).

	Total	New	Old
Modular forms	5312	1728	3584
Cusp forms	5056	1728	3328
Eisenstein series	256	0	256

Trace form

\( 1728 q + 48 q^{15} - 48 q^{27} + 64 q^{39} + 48 q^{42} + 80 q^{57} - 96 q^{59} + 96 q^{60} + 96 q^{62} + 48 q^{63} + 112 q^{75} + 192 q^{82} - 80 q^{87} - 192 q^{91} + 112 q^{93} - 80 q^{95} + 288 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1530, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1530, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(765, [\chi])\)\(^{\oplus 2}\)