↑

Properties

Label 1170.2.cp
Level $1170$
Weight $2$
Character orbit 1170.cp
Rep. character $\chi_{1170}(77,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $336$
Sturm bound $504$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.cp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 585 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1170, [\chi])\).

Total New Old
Modular forms 1040 336 704
Cusp forms 976 336 640
Eisenstein series 64 0 64

Trace form

\( 336 q + O(q^{10}) \) \( 336 q + 168 q^{16} + 48 q^{23} - 12 q^{27} + 24 q^{30} + 16 q^{36} + 72 q^{38} + 12 q^{42} + 96 q^{51} + 24 q^{65} + 16 q^{66} + 48 q^{75} + 96 q^{77} - 24 q^{78} - 32 q^{81} + 96 q^{82} - 24 q^{87} + 12 q^{90} - 48 q^{91} - 48 q^{92} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1170, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)