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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 19
190.2.a.a \(1\) \(1.517\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.b \(1\) \(1.517\) \(\Q\) None \(1\) \(-3\) \(-1\) \(-5\) \(-\) \(+\) \(-\) \(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}-5q^{7}+\cdots\)
190.2.a.c \(1\) \(1.517\) \(\Q\) None \(1\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.d \(2\) \(1.517\) \(\Q(\sqrt{17}) \) None \(-2\) \(-1\) \(2\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-\beta q^{7}+\cdots\)

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

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