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Properties

Label 1170.2.dj
Level $1170$
Weight $2$
Character orbit 1170.dj
Rep. character $\chi_{1170}(653,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $336$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.dj (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

\( 336 q + O(q^{10}) \) \( 336 q + 48 q^{11} + 168 q^{16} + 8 q^{18} + 8 q^{21} - 12 q^{27} + 12 q^{30} - 68 q^{33} + 36 q^{35} + 16 q^{36} - 36 q^{38} + 12 q^{42} + 20 q^{45} - 60 q^{47} - 8 q^{51} + 48 q^{57} + 16 q^{60} - 36 q^{62} - 76 q^{63} + 24 q^{65} + 16 q^{66} + 24 q^{71} - 8 q^{72} + 32 q^{75} - 96 q^{77} + 60 q^{78} + 8 q^{81} - 24 q^{82} + 120 q^{83} + 24 q^{85} - 8 q^{87} - 12 q^{90} - 24 q^{91} + 24 q^{92} - 68 q^{93} + 96 q^{97} + O(q^{100}) \)

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

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