Properties

Label 196.2.a
Level $196$
Weight $2$
Character orbit 196.a
Rep. character $\chi_{196}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $56$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 196.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(56\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(196))\).

Total New Old
Modular forms 40 4 36
Cusp forms 17 4 13
Eisenstein series 23 0 23

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

\(2\)\(7\)FrickeDim
\(-\)\(+\)$-$\(3\)
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(3\)

Trace form

\( 4 q + 6 q^{9} + O(q^{10}) \) \( 4 q + 6 q^{9} + 2 q^{11} - 2 q^{15} - 2 q^{23} + 2 q^{25} + 4 q^{29} - 18 q^{37} - 20 q^{39} - 16 q^{43} - 2 q^{51} + 26 q^{53} - 18 q^{57} + 24 q^{65} - 14 q^{67} - 10 q^{79} + 4 q^{81} + 22 q^{85} - 14 q^{93} + 2 q^{95} + 52 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(196))\) 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 7
196.2.a.a 196.a 1.a $1$ $1.565$ \(\Q\) None \(0\) \(-1\) \(-3\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
196.2.a.b 196.a 1.a $1$ $1.565$ \(\Q\) None \(0\) \(1\) \(3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
196.2.a.c 196.a 1.a $2$ $1.565$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}-\beta q^{5}+5q^{9}+4q^{11}-3\beta q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(196))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(196)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)