↑

Properties

Label 1530.2.bh
Level $1530$
Weight $2$
Character orbit 1530.bh
Rep. character $\chi_{1530}(53,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $144$
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.bh (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 255 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(648\)

Dimensions

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

Total New Old
Modular forms 1360 144 1216
Cusp forms 1232 144 1088
Eisenstein series 128 0 128

Trace form

\( 144 q - 144 q^{4} + O(q^{10}) \) \( 144 q - 144 q^{4} - 32 q^{13} + 144 q^{16} - 32 q^{22} - 8 q^{25} - 32 q^{31} + 24 q^{37} - 64 q^{49} + 32 q^{52} - 32 q^{55} + 8 q^{58} - 144 q^{64} + 32 q^{67} + 96 q^{70} + 40 q^{73} + 32 q^{79} - 56 q^{82} + 40 q^{85} + 32 q^{88} + 152 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(765, [\chi])\)\(^{\oplus 2}\)