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Properties

Label 1170.2.cg
Level $1170$
Weight $2$
Character orbit 1170.cg
Rep. character $\chi_{1170}(697,\cdot)$
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.cg (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

\( 336 q + 168 q^{4} + O(q^{10}) \) \( 336 q + 168 q^{4} - 8 q^{11} - 16 q^{15} - 168 q^{16} + 16 q^{18} - 8 q^{21} + 16 q^{23} + 12 q^{27} - 24 q^{30} - 24 q^{35} + 8 q^{39} - 16 q^{41} + 12 q^{42} - 16 q^{44} + 36 q^{45} - 40 q^{47} - 168 q^{49} + 8 q^{50} + 32 q^{59} - 8 q^{60} - 24 q^{62} - 336 q^{64} + 40 q^{65} - 16 q^{66} + 80 q^{69} + 16 q^{71} + 32 q^{72} + 56 q^{75} + 32 q^{77} - 8 q^{78} + 64 q^{81} - 96 q^{82} - 152 q^{83} - 16 q^{84} + 24 q^{85} + 64 q^{87} + 80 q^{90} - 16 q^{92} - 32 q^{93} - 24 q^{99} + O(q^{100}) \)

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

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