Properties

Label 1328.1.g
Level $1328$
Weight $1$
Character orbit 1328.g
Rep. character $\chi_{1328}(497,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1328 = 2^{4} \cdot 83 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1328.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 83 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1328, [\chi])\).

Total New Old
Modular forms 24 5 19
Cusp forms 18 4 14
Eisenstein series 6 1 5

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

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

Trace form

\( 4 q + q^{3} + q^{7} + 3 q^{9} + O(q^{10}) \) \( 4 q + q^{3} + q^{7} + 3 q^{9} + q^{11} - q^{17} - 2 q^{21} + q^{23} + 4 q^{25} + 2 q^{27} - q^{29} + q^{31} - 2 q^{33} - q^{37} - q^{41} + 3 q^{49} + 2 q^{51} + q^{59} - q^{61} + 3 q^{63} - 2 q^{69} + q^{75} - 2 q^{77} + 2 q^{81} - 4 q^{83} - 7 q^{87} - 2 q^{93} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1328, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1328.1.g.a 1328.g 83.b $1$ $0.663$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(1\) \(0\) \(1\) \(q+q^{3}+q^{7}+q^{11}-q^{17}+q^{21}-2q^{23}+\cdots\)
1328.1.g.b 1328.g 83.b $3$ $0.663$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1328, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1328, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(83, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(332, [\chi])\)\(^{\oplus 3}\)