Properties

Label 608.1.o
Level $608$
Weight $1$
Character orbit 608.o
Rep. character $\chi_{608}(239,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 608.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(608, [\chi])\).

Total New Old
Modular forms 24 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q - q^{3} + O(q^{10}) \) \( 2 q - q^{3} + 2 q^{11} - 2 q^{17} + q^{19} - q^{25} - 2 q^{27} - q^{33} + q^{41} + 2 q^{43} + 2 q^{49} - 2 q^{51} - 2 q^{57} - q^{59} - q^{67} + q^{73} + 2 q^{75} + q^{81} + 2 q^{83} - 2 q^{89} + q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
608.1.o.a 608.o 152.k $2$ $0.303$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{3}+q^{11}+\zeta_{6}^{2}q^{17}+\zeta_{6}q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(608, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(608, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)