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Properties

Label 608.3.o
Level $608$
Weight $3$
Character orbit 608.o
Rep. character $\chi_{608}(239,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $2$
Sturm bound $240$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 608.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(608, [\chi])\).

Total New Old
Modular forms 336 84 252
Cusp forms 304 76 228
Eisenstein series 32 8 24

Trace form

\( 76 q + 2 q^{3} - 104 q^{9} + 8 q^{11} - 2 q^{17} - 28 q^{19} + 148 q^{25} - 28 q^{27} - 4 q^{33} - 144 q^{35} - 26 q^{41} + 2 q^{43} - 404 q^{49} - 130 q^{51} - 74 q^{57} + 2 q^{59} - 108 q^{65} + 290 q^{67}+ \cdots + 222 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
608.3.o.a 608.o 152.k $4$ $16.567$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) 152.3.k.a \(0\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(\beta _{1}-\beta _{2})q^{3}+(-2^{4}+2^{4}\beta _{1}-2\beta _{2}+\cdots)q^{9}+\cdots\)
608.3.o.b 608.o 152.k $72$ $16.567$ None 152.3.k.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(608, [\chi])\) into lower level spaces

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