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Properties

Label 190.2.a
Level $190$
Weight $2$
Character orbit 190.a
Rep. character $\chi_{190}(1,\cdot)$
Character field $\Q$
Dimension $5$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(190))\).

Total New Old
Modular forms 34 5 29
Cusp forms 27 5 22
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(19\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(-\)\(+\)$-$\(2\)
\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(-\)$-$\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(3\)

Trace form

\( 5 q - q^{2} - 4 q^{3} + 5 q^{4} + q^{5} - 8 q^{7} - q^{8} + 5 q^{9} + O(q^{10}) \) \( 5 q - q^{2} - 4 q^{3} + 5 q^{4} + q^{5} - 8 q^{7} - q^{8} + 5 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{14} + 4 q^{15} + 5 q^{16} - 2 q^{17} + 3 q^{18} - q^{19} + q^{20} + 24 q^{21} - 12 q^{22} + 8 q^{23} + 5 q^{25} + 2 q^{26} - 16 q^{27} - 8 q^{28} - 10 q^{29} + 4 q^{30} + 8 q^{31} - q^{32} + 8 q^{33} - 10 q^{34} + 4 q^{35} + 5 q^{36} - 22 q^{37} + 5 q^{38} - 20 q^{39} - q^{40} + 10 q^{41} + 4 q^{42} + 4 q^{44} - 3 q^{45} + 12 q^{46} - 4 q^{47} - 4 q^{48} + q^{49} - q^{50} + 16 q^{51} - 6 q^{52} - 6 q^{53} - 12 q^{54} + 12 q^{55} - 4 q^{56} - 2 q^{58} - 12 q^{59} + 4 q^{60} + 6 q^{61} - 8 q^{62} - 36 q^{63} + 5 q^{64} + 2 q^{65} + 16 q^{66} - 4 q^{67} - 2 q^{68} - 40 q^{69} + 4 q^{70} + 16 q^{71} + 3 q^{72} - 2 q^{73} - 2 q^{74} - 4 q^{75} - q^{76} + 16 q^{77} + 24 q^{78} + q^{80} - 3 q^{81} - 10 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} + 2 q^{89} - 13 q^{90} - 16 q^{91} + 8 q^{92} + 16 q^{93} + 4 q^{94} - q^{95} - 18 q^{97} + 23 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(190))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 19
190.2.a.a 190.a 1.a $1$ $1.517$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.b 190.a 1.a $1$ $1.517$ \(\Q\) None \(1\) \(-3\) \(-1\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}-5q^{7}+\cdots\)
190.2.a.c 190.a 1.a $1$ $1.517$ \(\Q\) None \(1\) \(1\) \(1\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.d 190.a 1.a $2$ $1.517$ \(\Q(\sqrt{17}) \) None \(-2\) \(-1\) \(2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-\beta q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(190))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(190)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)