↑

Properties

Label 1530.2.ci
Level $1530$
Weight $2$
Character orbit 1530.ci
Rep. character $\chi_{1530}(257,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $864$
Sturm bound $648$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1530.ci (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 765 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(648\)

Dimensions

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

Total New Old
Modular forms 2656 864 1792
Cusp forms 2528 864 1664
Eisenstein series 128 0 128

Trace form

\( 864 q - 432 q^{4} + O(q^{10}) \) \( 864 q - 432 q^{4} - 24 q^{15} - 432 q^{16} - 32 q^{39} + 48 q^{42} - 24 q^{45} - 16 q^{51} + 88 q^{57} + 144 q^{59} + 48 q^{60} + 88 q^{63} + 864 q^{64} - 168 q^{65} - 48 q^{79} - 96 q^{82} + 48 q^{85} + 72 q^{90} + 96 q^{91} + 48 q^{95} + 48 q^{97} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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