Properties

Label 196.2.a
Level 196
Weight 2
Character orbit a
Rep. character \(\chi_{196}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 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: \(\Q\)
Newforms: \( 3 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(196))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
196.2.a.a \(1\) \(1.565\) \(\Q\) None \(0\) \(-1\) \(-3\) \(0\) \(-\) \(-\) \(q-q^{3}-3q^{5}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
196.2.a.b \(1\) \(1.565\) \(\Q\) None \(0\) \(1\) \(3\) \(0\) \(-\) \(+\) \(q+q^{3}+3q^{5}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
196.2.a.c \(2\) \(1.565\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+2\beta q^{3}-\beta q^{5}+5q^{9}+4q^{11}-3\beta q^{13}+\cdots\)

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

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