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Properties

Label 208.2.k
Level $208$
Weight $2$
Character orbit 208.k
Rep. character $\chi_{208}(31,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $14$
Newform subspaces $2$
Sturm bound $56$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 208 = 2^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 208.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(208, [\chi])\).

Total New Old
Modular forms 68 14 54
Cusp forms 44 14 30
Eisenstein series 24 0 24

Trace form

\( 14 q + 6 q^{5} - 14 q^{9} + O(q^{10}) \) \( 14 q + 6 q^{5} - 14 q^{9} - 8 q^{21} + 38 q^{37} + 18 q^{41} - 30 q^{45} - 36 q^{53} - 56 q^{57} - 36 q^{61} - 30 q^{65} + 14 q^{73} + 14 q^{81} + 36 q^{85} - 6 q^{89} + 56 q^{93} + 22 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(208, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
208.2.k.a 208.k 52.f $2$ $1.661$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+i)q^{5}+3q^{9}+(2+3i)q^{13}-2iq^{17}+\cdots\)
208.2.k.b 208.k 52.f $12$ $1.661$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}-\beta _{6}q^{5}-\beta _{11}q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(208, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(208, [\chi]) \cong \)