Properties

Label 3528.1.ce
Level $3528$
Weight $1$
Character orbit 3528.ce
Rep. character $\chi_{3528}(2419,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $5$
Sturm bound $672$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3528.ce (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(672\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3528, [\chi])\).

Total New Old
Modular forms 60 36 24
Cusp forms 28 20 8
Eisenstein series 32 16 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 4 0 0

Trace form

\( 20 q + 4 q^{3} + 12 q^{4} + 4 q^{9} + O(q^{10}) \) \( 20 q + 4 q^{3} + 12 q^{4} + 4 q^{9} - 2 q^{10} + 2 q^{11} - 4 q^{12} + 20 q^{16} - 2 q^{17} + 2 q^{19} - 8 q^{25} - 2 q^{26} + 4 q^{27} - 2 q^{30} + 2 q^{33} - 4 q^{36} + 2 q^{40} - 2 q^{41} + 2 q^{43} - 2 q^{44} + 2 q^{46} + 4 q^{48} - 2 q^{51} + 2 q^{57} + 2 q^{58} + 12 q^{64} - 4 q^{65} + 2 q^{68} + 2 q^{73} + 2 q^{74} - 2 q^{76} - 2 q^{78} + 4 q^{81} - 2 q^{83} + 2 q^{89} - 2 q^{90} + 2 q^{97} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3528.1.ce.a 3528.ce 504.be $2$ $1.761$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(2\) \(-1\) \(0\) \(0\) \(q+q^{2}+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{6}+q^{8}+\cdots\)
3528.1.ce.b 3528.ce 504.be $2$ $1.761$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(2\) \(1\) \(0\) \(0\) \(q+q^{2}-\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}^{2}q^{6}+q^{8}+\cdots\)
3528.1.ce.c 3528.ce 504.be $4$ $1.761$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}+q^{3}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{6}+\cdots\)
3528.1.ce.d 3528.ce 504.be $4$ $1.761$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-2}) \) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+\zeta_{12}^{5}q^{3}+q^{4}+\zeta_{12}^{5}q^{6}+\cdots\)
3528.1.ce.e 3528.ce 504.be $8$ $1.761$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-2}) \) None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}-\zeta_{24}^{7}q^{3}+q^{4}+\zeta_{24}^{7}q^{6}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)