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Properties

Label 1064.2.dc
Level $1064$
Weight $2$
Character orbit 1064.dc
Rep. character $\chi_{1064}(169,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $180$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.dc (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1064, [\chi])\).

Total New Old
Modular forms 1008 180 828
Cusp forms 912 180 732
Eisenstein series 96 0 96

Trace form

\( 180 q - 6 q^{3} + 18 q^{9} + O(q^{10}) \) \( 180 q - 6 q^{3} + 18 q^{9} - 12 q^{15} - 12 q^{23} - 12 q^{25} + 6 q^{27} + 12 q^{31} + 90 q^{33} + 24 q^{37} + 42 q^{41} + 36 q^{45} - 90 q^{49} - 30 q^{51} + 72 q^{55} - 12 q^{57} - 42 q^{59} - 48 q^{65} - 162 q^{67} - 108 q^{71} - 120 q^{73} - 36 q^{79} - 138 q^{81} - 36 q^{83} + 36 q^{85} - 72 q^{87} - 36 q^{93} + 24 q^{95} + 90 q^{97} + 66 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1064, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1064, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1064, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)