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Properties

Label 1512.1.bd
Level $1512$
Weight $1$
Character orbit 1512.bd
Rep. character $\chi_{1512}(53,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $4$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1512.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(5\)

Dimensions

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

Total New Old
Modular forms 44 8 36
Cusp forms 20 8 12
Eisenstein series 24 0 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - 4 q^{4} + 2 q^{7} + O(q^{10}) \) \( 8 q - 4 q^{4} + 2 q^{7} - 2 q^{10} - 4 q^{16} + 4 q^{22} - 6 q^{25} + 2 q^{28} - 2 q^{31} - 2 q^{40} + 2 q^{49} - 16 q^{55} + 4 q^{58} + 8 q^{64} + 10 q^{70} + 4 q^{73} + 4 q^{79} - 2 q^{88} + 4 q^{97} + O(q^{100}) \)

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.bd.a 1512.bd 168.s $2$ $0.755$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-6}) \) None \(-1\) \(0\) \(-2\) \(-1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots\)
1512.1.bd.b 1512.bd 168.s $2$ $0.755$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-6}) \) None \(-1\) \(0\) \(1\) \(2\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{7}+\cdots\)
1512.1.bd.c 1512.bd 168.s $2$ $0.755$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-6}) \) None \(1\) \(0\) \(-1\) \(2\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+q^{7}+\cdots\)
1512.1.bd.d 1512.bd 168.s $2$ $0.755$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-6}) \) None \(1\) \(0\) \(2\) \(-1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)