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Properties

Label 190.2.k
Level $190$
Weight $2$
Character orbit 190.k
Rep. character $\chi_{190}(61,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $48$
Newform subspaces $4$
Sturm bound $60$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 190.k (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 4 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(190, [\chi])\).

Total New Old
Modular forms 204 48 156
Cusp forms 156 48 108
Eisenstein series 48 0 48

Trace form

\( 48 q + 6 q^{3} + 6 q^{6} + 6 q^{8} + 6 q^{9} + O(q^{10}) \) \( 48 q + 6 q^{3} + 6 q^{6} + 6 q^{8} + 6 q^{9} - 24 q^{13} - 12 q^{14} - 12 q^{17} - 36 q^{18} + 12 q^{19} - 24 q^{22} - 24 q^{23} + 6 q^{24} - 6 q^{26} - 6 q^{27} + 12 q^{28} + 12 q^{29} - 12 q^{31} + 42 q^{33} + 24 q^{34} + 6 q^{35} + 6 q^{36} + 24 q^{37} + 18 q^{38} - 24 q^{39} - 12 q^{41} + 24 q^{42} + 36 q^{43} - 6 q^{44} - 84 q^{47} - 12 q^{48} - 60 q^{49} + 6 q^{50} + 18 q^{51} + 12 q^{52} - 84 q^{53} - 54 q^{54} + 24 q^{56} - 84 q^{57} - 48 q^{58} - 78 q^{59} + 60 q^{61} - 60 q^{62} - 60 q^{63} - 24 q^{64} + 18 q^{65} + 30 q^{66} + 18 q^{67} - 6 q^{68} - 36 q^{69} + 36 q^{71} - 12 q^{72} + 24 q^{73} + 18 q^{74} + 6 q^{76} + 72 q^{77} + 36 q^{78} + 72 q^{79} - 6 q^{81} + 42 q^{82} + 36 q^{83} + 84 q^{87} + 12 q^{88} + 84 q^{89} + 24 q^{90} + 12 q^{91} + 12 q^{92} + 72 q^{93} + 60 q^{94} + 18 q^{97} + 24 q^{98} + 144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(190, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
190.2.k.a 190.k 19.e $6$ $1.517$ \(\Q(\zeta_{18})\) None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
190.2.k.b 190.k 19.e $12$ $1.517$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
190.2.k.c 190.k 19.e $12$ $1.517$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{8}q^{2}+(1+\beta _{4}+\beta _{7}+\beta _{10}-\beta _{11})q^{3}+\cdots\)
190.2.k.d 190.k 19.e $18$ $1.517$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{9}q^{2}-\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(190, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(190, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)