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Properties

Label 3528.1.cg
Level $3528$
Weight $1$
Character orbit 3528.cg
Rep. character $\chi_{3528}(2059,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $22$
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.cg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
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 42 18
Cusp forms 28 22 6
Eisenstein series 32 20 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 8 0 0

Trace form

\( 22 q + q^{2} + q^{3} - 3 q^{4} + q^{6} - 2 q^{8} - 3 q^{9} + O(q^{10}) \) \( 22 q + q^{2} + q^{3} - 3 q^{4} + q^{6} - 2 q^{8} - 3 q^{9} + 3 q^{11} - 2 q^{12} - 11 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} - q^{22} + q^{24} - 7 q^{25} - 2 q^{27} - 4 q^{30} + q^{32} - q^{33} - q^{34} - 7 q^{36} - q^{38} - q^{41} + 3 q^{43} + 10 q^{44} - 8 q^{46} + q^{48} + q^{50} - 5 q^{51} + q^{54} + 3 q^{57} + 4 q^{58} - q^{59} + 6 q^{64} + 4 q^{65} + 2 q^{66} - q^{67} - q^{68} + q^{72} + 2 q^{73} + 4 q^{74} + q^{75} - q^{76} - 4 q^{78} - 3 q^{81} + 2 q^{82} + 2 q^{83} - q^{86} - q^{88} - 4 q^{89} - 2 q^{96} - q^{97} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.cg.a 3528.cg 72.p $2$ $1.761$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots\)
3528.1.cg.b 3528.cg 72.p $4$ $1.761$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{6}+\cdots\)
3528.1.cg.c 3528.cg 72.p $4$ $1.761$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
3528.1.cg.d 3528.cg 72.p $4$ $1.761$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{5}+\cdots\)
3528.1.cg.e 3528.cg 72.p $8$ $1.761$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-2}) \) None \(4\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{8}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{4}q^{4}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)