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Properties

Label 1134.2.w
Level $1134$
Weight $2$
Character orbit 1134.w
Rep. character $\chi_{1134}(37,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $144$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.w (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1134, [\chi])\).

Total New Old
Modular forms 1368 144 1224
Cusp forms 1224 144 1080
Eisenstein series 144 0 144

Trace form

\( 144 q + O(q^{10}) \) \( 144 q + 12 q^{11} + 6 q^{14} - 48 q^{17} - 6 q^{23} + 36 q^{26} - 6 q^{29} - 18 q^{35} + 12 q^{41} - 18 q^{47} - 18 q^{49} - 12 q^{50} + 30 q^{53} - 12 q^{56} - 30 q^{59} - 36 q^{61} + 48 q^{62} - 72 q^{64} + 108 q^{65} + 36 q^{68} - 18 q^{70} - 24 q^{71} - 36 q^{73} - 18 q^{74} + 102 q^{77} - 36 q^{79} + 12 q^{80} + 72 q^{85} + 24 q^{86} - 144 q^{89} - 18 q^{91} - 42 q^{92} - 36 q^{94} - 114 q^{95} - 12 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1134, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1134, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1134, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)