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Properties

Label 1170.2.cx
Level $1170$
Weight $2$
Character orbit 1170.cx
Rep. character $\chi_{1170}(41,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $224$
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.cx (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
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 224 816
Cusp forms 976 224 752
Eisenstein series 64 0 64

Trace form

\( 224 q + 16 q^{7} + O(q^{10}) \) \( 224 q + 16 q^{7} + 24 q^{11} + 8 q^{15} + 112 q^{16} - 32 q^{18} + 16 q^{19} + 40 q^{21} - 48 q^{27} + 8 q^{28} + 8 q^{31} + 8 q^{33} + 8 q^{37} + 8 q^{39} + 48 q^{41} + 48 q^{42} + 32 q^{45} + 72 q^{47} - 16 q^{52} + 24 q^{54} - 48 q^{57} - 16 q^{60} + 8 q^{63} + 16 q^{66} - 56 q^{67} + 24 q^{71} + 16 q^{72} - 56 q^{73} - 8 q^{76} - 48 q^{77} + 48 q^{78} + 24 q^{79} - 8 q^{81} + 72 q^{83} + 8 q^{84} + 24 q^{85} + 64 q^{87} - 120 q^{89} - 8 q^{91} - 8 q^{93} + 8 q^{97} - 96 q^{98} - 144 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)