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Properties

Label 1512.1.ce
Level $1512$
Weight $1$
Character orbit 1512.ce
Rep. character $\chi_{1512}(235,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1512.ce (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1512, [\chi])\).

Total New Old
Modular forms 36 12 24
Cusp forms 12 4 8
Eisenstein series 24 8 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 4 0 0

Trace form

\( 4 q - 4 q^{4} + O(q^{10}) \) \( 4 q - 4 q^{4} + 2 q^{10} - 2 q^{11} - 4 q^{14} + 4 q^{16} - 2 q^{17} - 2 q^{19} - 2 q^{26} + 2 q^{35} - 2 q^{40} - 2 q^{41} + 2 q^{43} + 2 q^{44} + 2 q^{46} - 4 q^{49} + 4 q^{56} + 2 q^{58} - 4 q^{64} + 4 q^{65} + 2 q^{68} - 2 q^{73} - 2 q^{74} + 2 q^{76} - 2 q^{83} + 2 q^{89} - 2 q^{91} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1512.1.ce.a 1512.ce 504.be $4$ $0.755$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)