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Properties

Label 608.6.b
Level $608$
Weight $6$
Character orbit 608.b
Rep. character $\chi_{608}(303,\cdot)$
Character field $\Q$
Dimension $98$
Newform subspaces $2$
Sturm bound $480$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 608.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(480\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(608, [\chi])\).

Total New Old
Modular forms 408 102 306
Cusp forms 392 98 294
Eisenstein series 16 4 12

Trace form

\( 98 q - 7618 q^{9} + O(q^{10}) \) \( 98 q - 7618 q^{9} + 4 q^{11} - 4 q^{17} - 2358 q^{19} - 56254 q^{25} - 7720 q^{35} + 4 q^{43} - 177226 q^{49} + 3000 q^{57} - 105140 q^{73} + 560178 q^{81} + 126444 q^{83} + 65468 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
608.6.b.a 608.b 152.b $2$ $97.513$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) 152.6.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+22\beta q^{3}-725q^{9}+474q^{11}+1914q^{17}+\cdots\)
608.6.b.b 608.b 152.b $96$ $97.513$ None 152.6.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(608, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(608, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)