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Properties

Label 206.2.c
Level $206$
Weight $2$
Character orbit 206.c
Rep. character $\chi_{206}(149,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $3$
Sturm bound $52$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 206 = 2 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 206.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 103 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(52\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(206, [\chi])\).

Total New Old
Modular forms 56 16 40
Cusp forms 48 16 32
Eisenstein series 8 0 8

Trace form

\( 16 q - 4 q^{3} - 8 q^{4} - 6 q^{5} + 4 q^{7} + 20 q^{9} + O(q^{10}) \) \( 16 q - 4 q^{3} - 8 q^{4} - 6 q^{5} + 4 q^{7} + 20 q^{9} + 12 q^{10} + 6 q^{11} + 2 q^{12} + 20 q^{13} - 8 q^{14} - 4 q^{15} - 8 q^{16} - 2 q^{17} - 16 q^{19} - 6 q^{20} - 22 q^{21} - 8 q^{22} + 20 q^{23} - 12 q^{25} - 2 q^{26} - 4 q^{27} + 4 q^{28} + 6 q^{29} - 12 q^{30} + 8 q^{31} + 12 q^{33} + 2 q^{35} - 10 q^{36} - 28 q^{37} + 4 q^{38} - 8 q^{39} - 6 q^{40} - 6 q^{41} + 4 q^{42} - 8 q^{43} + 6 q^{44} - 12 q^{45} + 18 q^{46} + 2 q^{48} + 8 q^{49} - 12 q^{51} - 10 q^{52} + 10 q^{53} - 18 q^{54} + 4 q^{56} - 4 q^{57} - 6 q^{58} - 4 q^{59} - 4 q^{60} + 8 q^{61} + 46 q^{63} + 16 q^{64} - 16 q^{65} + 8 q^{66} + 2 q^{67} - 2 q^{68} - 88 q^{69} + 24 q^{70} - 12 q^{71} - 8 q^{73} - 28 q^{74} + 22 q^{75} + 32 q^{76} - 12 q^{77} - 2 q^{78} + 12 q^{79} + 12 q^{80} - 16 q^{81} + 12 q^{82} + 34 q^{83} - 22 q^{84} + 6 q^{85} - 18 q^{86} + 18 q^{87} + 4 q^{88} + 24 q^{89} + 104 q^{90} + 6 q^{91} - 10 q^{92} - 80 q^{93} - 92 q^{95} + 36 q^{97} - 28 q^{98} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(206, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
206.2.c.a 206.c 103.c $2$ $1.645$ \(\Q(\sqrt{-3}) \) None \(1\) \(4\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+2q^{3}+(-1+\zeta_{6})q^{4}+(2+\cdots)q^{5}+\cdots\)
206.2.c.b 206.c 103.c $6$ $1.645$ 6.0.1783323.2 None \(3\) \(-6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{4})q^{2}+(-1-\beta _{3})q^{3}-\beta _{4}q^{4}+\cdots\)
206.2.c.c 206.c 103.c $8$ $1.645$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(-2\) \(-6\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{4})q^{2}-\beta _{2}q^{3}-\beta _{4}q^{4}+(1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(206, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(206, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(103, [\chi])\)\(^{\oplus 2}\)