Properties

Label 2028.1.s
Level $2028$
Weight $1$
Character orbit 2028.s
Rep. character $\chi_{2028}(485,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $2$
Sturm bound $364$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2028.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(364\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2028, [\chi])\).

Total New Old
Modular forms 100 6 94
Cusp forms 16 6 10
Eisenstein series 84 0 84

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q - q^{3} + 3 q^{7} - 3 q^{9} + O(q^{10}) \) \( 6 q - q^{3} + 3 q^{7} - 3 q^{9} - 6 q^{25} + 2 q^{27} - q^{43} + 2 q^{49} + q^{61} - 3 q^{63} - 3 q^{67} + q^{75} - 2 q^{79} - 3 q^{81} + 3 q^{93} + 3 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2028, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2028.1.s.a 2028.s 39.h $2$ $1.012$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(3\) \(q+\zeta_{6}q^{3}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\cdots)q^{21}+\cdots\)
2028.1.s.b 2028.s 39.h $4$ $1.012$ \(\Q(\zeta_{12})\) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{2}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2028, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2028, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 3}\)