Properties

Label 1170.2.da
Level $1170$
Weight $2$
Character orbit 1170.da
Rep. character $\chi_{1170}(59,\cdot)$
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.da (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

\( 336 q + O(q^{10}) \) \( 336 q - 8 q^{15} - 336 q^{16} + 16 q^{21} - 96 q^{35} - 24 q^{36} - 24 q^{39} - 48 q^{41} + 12 q^{45} + 24 q^{50} - 48 q^{54} + 8 q^{60} + 120 q^{65} + 16 q^{66} + 24 q^{71} - 48 q^{74} + 24 q^{79} + 104 q^{81} - 8 q^{84} + 24 q^{85} + 120 q^{89} - 32 q^{99} + O(q^{100}) \)

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

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