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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
190.2.k.a \(6\) \(1.517\) \(\Q(\zeta_{18})\) None \(0\) \(3\) \(0\) \(0\) \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
190.2.k.b \(12\) \(1.517\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(6\) \(q+(-\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
190.2.k.c \(12\) \(1.517\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(0\) \(-6\) \(q-\beta _{8}q^{2}+(1+\beta _{4}+\beta _{7}+\beta _{10}-\beta _{11})q^{3}+\cdots\)
190.2.k.d \(18\) \(1.517\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}-\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{10}q^{5}+\cdots\)

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

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