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Properties

Label 1134.2.bh
Level $1134$
Weight $2$
Character orbit 1134.bh
Rep. character $\chi_{1134}(43,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $972$
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.bh (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 3960 972 2988
Cusp forms 3816 972 2844
Eisenstein series 144 0 144

Trace form

\( 972 q + O(q^{10}) \) \( 972 q + 18 q^{18} + 36 q^{20} + 108 q^{27} + 108 q^{29} + 36 q^{36} + 18 q^{38} + 108 q^{45} + 126 q^{51} + 108 q^{53} + 108 q^{57} + 126 q^{59} + 36 q^{65} + 108 q^{67} - 36 q^{68} - 288 q^{69} - 144 q^{71} - 72 q^{72} - 288 q^{74} - 360 q^{75} + 54 q^{76} - 144 q^{78} + 108 q^{79} - 288 q^{81} - 288 q^{83} + 108 q^{85} - 144 q^{86} + 54 q^{88} - 342 q^{89} - 288 q^{90} - 72 q^{92} - 108 q^{93} - 288 q^{95} - 36 q^{96} + 108 q^{97} - 72 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1134, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)