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Properties

Label 1170.2.bt
Level $1170$
Weight $2$
Character orbit 1170.bt
Rep. character $\chi_{1170}(571,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
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.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 520 112 408
Cusp forms 488 112 376
Eisenstein series 32 0 32

Trace form

\( 112 q + 56 q^{4} + 16 q^{9} + O(q^{10}) \) \( 112 q + 56 q^{4} + 16 q^{9} - 4 q^{13} - 56 q^{16} - 32 q^{17} + 56 q^{25} - 16 q^{26} - 48 q^{27} + 40 q^{29} + 16 q^{35} + 8 q^{36} + 24 q^{38} - 28 q^{39} + 8 q^{42} + 8 q^{43} + 64 q^{49} - 32 q^{51} + 4 q^{52} + 80 q^{53} - 56 q^{61} - 112 q^{62} - 112 q^{64} + 4 q^{65} + 40 q^{66} - 16 q^{68} + 104 q^{69} + 16 q^{74} + 16 q^{77} + 28 q^{78} - 32 q^{79} - 32 q^{81} - 32 q^{87} + 16 q^{90} + 24 q^{91} + 16 q^{95} + O(q^{100}) \)

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

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