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Properties

Label 190.2.r
Level $190$
Weight $2$
Character orbit 190.r
Rep. character $\chi_{190}(3,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $120$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 190.r (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 408 120 288
Cusp forms 312 120 192
Eisenstein series 96 0 96

Trace form

\( 120 q - 12 q^{7} + O(q^{10}) \) \( 120 q - 12 q^{7} - 36 q^{15} + 36 q^{17} - 96 q^{21} + 24 q^{22} - 24 q^{25} - 12 q^{26} - 96 q^{33} + 36 q^{35} - 12 q^{41} - 72 q^{43} - 36 q^{45} - 24 q^{47} - 144 q^{50} + 24 q^{51} + 36 q^{53} - 72 q^{55} + 84 q^{57} - 24 q^{60} + 48 q^{61} - 24 q^{62} + 36 q^{63} - 180 q^{65} - 24 q^{66} - 96 q^{67} - 12 q^{68} - 48 q^{70} - 36 q^{73} + 12 q^{76} + 96 q^{78} + 144 q^{81} + 48 q^{82} + 24 q^{83} + 48 q^{85} + 48 q^{86} + 72 q^{87} + 168 q^{90} + 72 q^{91} + 72 q^{92} + 156 q^{93} + 24 q^{95} + 120 q^{97} + 24 q^{98} + O(q^{100}) \)

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.r.a 190.r 95.r $120$ $1.517$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{36}]$

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

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