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

\( 5 q - q^{2} - 4 q^{3} + 5 q^{4} + q^{5} - 8 q^{7} - q^{8} + 5 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{14} + 4 q^{15} + 5 q^{16} - 2 q^{17} + 3 q^{18} - q^{19} + q^{20} + 24 q^{21} - 12 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

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

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

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