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Properties

Label 608.2.s
Level $608$
Weight $2$
Character orbit 608.s
Rep. character $\chi_{608}(335,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
Newform subspaces $3$
Sturm bound $160$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 608.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(160\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(608, [\chi])\).

Total New Old
Modular forms 176 44 132
Cusp forms 144 36 108
Eisenstein series 32 8 24

Trace form

\( 36 q + 6 q^{3} + 12 q^{9} + O(q^{10}) \) \( 36 q + 6 q^{3} + 12 q^{9} + 8 q^{11} - 2 q^{17} - 4 q^{19} + 8 q^{25} - 24 q^{33} + 16 q^{35} + 6 q^{41} + 2 q^{43} - 36 q^{49} + 30 q^{51} - 14 q^{57} + 6 q^{59} + 6 q^{67} + 6 q^{73} - 2 q^{81} - 32 q^{83} - 6 q^{89} - 36 q^{91} - 6 q^{97} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
608.2.s.a 608.s 152.o $4$ $4.855$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) \(0\) \(-6\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
608.2.s.b 608.s 152.o $4$ $4.855$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2+\beta _{2})q^{3}+(\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{3})q^{7}+\cdots\)
608.2.s.c 608.s 152.o $28$ $4.855$ None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(608, [\chi])\) into lower level spaces

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