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Properties

Label 190.2.e
Level $190$
Weight $2$
Character orbit 190.e
Rep. character $\chi_{190}(11,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $3$
Sturm bound $60$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 68 8 60
Cusp forms 52 8 44
Eisenstein series 16 0 16

Trace form

\( 8 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - 2 q^{6} + 16 q^{7} - 4 q^{8} + 2 q^{9} + O(q^{10}) \) \( 8 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - 2 q^{6} + 16 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{10} + 8 q^{11} - 4 q^{12} - 4 q^{13} + 6 q^{14} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 4 q^{19} - 4 q^{21} - 6 q^{22} + 4 q^{23} - 2 q^{24} - 4 q^{25} - 4 q^{27} - 8 q^{28} - 8 q^{29} + 2 q^{32} - 2 q^{33} + 4 q^{34} - 2 q^{35} + 2 q^{36} - 4 q^{38} - 8 q^{39} + 2 q^{40} + 8 q^{41} + 4 q^{42} - 4 q^{43} - 4 q^{44} + 16 q^{45} + 12 q^{46} - 8 q^{47} + 2 q^{48} - 4 q^{49} - 4 q^{50} + 20 q^{51} - 4 q^{52} - 2 q^{54} - 12 q^{56} - 20 q^{57} + 8 q^{58} - 30 q^{59} - 16 q^{61} - 8 q^{62} + 8 q^{63} + 8 q^{64} - 24 q^{65} + 2 q^{66} - 30 q^{67} + 8 q^{68} + 64 q^{69} + 4 q^{70} - 16 q^{71} + 4 q^{72} - 14 q^{73} + 22 q^{74} - 4 q^{75} + 14 q^{76} + 8 q^{77} - 4 q^{78} - 4 q^{79} + 4 q^{81} + 10 q^{82} + 4 q^{83} + 8 q^{84} - 8 q^{86} + 12 q^{88} - 14 q^{89} + 2 q^{90} - 4 q^{91} + 4 q^{92} + 28 q^{93} - 16 q^{94} + 20 q^{95} + 4 q^{96} + 26 q^{97} + 10 q^{98} + 6 q^{99} + O(q^{100}) \)

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.e.a 190.e 19.c $2$ $1.517$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
190.2.e.b 190.e 19.c $2$ $1.517$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
190.2.e.c 190.e 19.c $4$ $1.517$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(1\) \(-2\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)

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

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