Properties

Label 2144.1.bu
Level $2144$
Weight $1$
Character orbit 2144.bu
Rep. character $\chi_{2144}(47,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $20$
Newform subspaces $1$
Sturm bound $272$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2144 = 2^{5} \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2144.bu (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 536 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(272\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2144, [\chi])\).

Total New Old
Modular forms 240 60 180
Cusp forms 80 20 60
Eisenstein series 160 40 120

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q - 2 q^{3} + O(q^{10}) \) \( 20 q - 2 q^{3} - 2 q^{11} - 12 q^{17} + q^{19} - 2 q^{25} + 2 q^{27} - 2 q^{33} + 2 q^{41} - 2 q^{43} + q^{49} - q^{51} + q^{57} + 9 q^{59} + 2 q^{67} - q^{73} + 9 q^{75} + 2 q^{81} + 9 q^{83} + 2 q^{89} - q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2144, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2144.1.bu.a 2144.bu 536.aa $20$ $1.070$ \(\Q(\zeta_{33})\) $D_{33}$ \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-\zeta_{66}^{8}+\zeta_{66}^{13})q^{3}+(\zeta_{66}^{16}-\zeta_{66}^{21}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2144, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2144, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(536, [\chi])\)\(^{\oplus 3}\)