Properties

Label 164.2.a
Level 164
Weight 2
Character orbit a
Rep. character \(\chi_{164}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 42
Trace bound 0

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Defining parameters

Level: \( N \) = \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 164.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(42\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(164))\).

Total New Old
Modular forms 24 4 20
Cusp forms 19 4 15
Eisenstein series 5 0 5

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

\(2\)\(41\)FrickeDim.
\(-\)\(+\)\(-\)\(4\)
Plus space\(+\)\(0\)
Minus space\(-\)\(4\)

Trace form

\( 4q + 2q^{3} + 4q^{5} + 12q^{9} + O(q^{10}) \) \( 4q + 2q^{3} + 4q^{5} + 12q^{9} + 4q^{11} - 10q^{15} - 4q^{17} + 6q^{19} - 12q^{23} + 12q^{25} - 10q^{27} - 4q^{29} - 8q^{31} - 20q^{33} - 26q^{35} + 16q^{37} - 24q^{39} - 4q^{41} + 4q^{43} + 4q^{45} - 6q^{47} + 16q^{49} - 4q^{51} - 16q^{53} - 2q^{55} + 4q^{57} + 12q^{59} + 24q^{61} - 10q^{63} + 4q^{65} + 28q^{67} - 28q^{69} - 2q^{71} + 8q^{73} + 30q^{75} + 8q^{77} - 18q^{79} + 28q^{81} - 12q^{83} + 32q^{85} + 44q^{87} + 4q^{89} + 36q^{91} - 28q^{93} + 14q^{95} + 16q^{97} + 58q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(164))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 41
164.2.a.a \(4\) \(1.310\) 4.4.25808.1 None \(0\) \(2\) \(4\) \(0\) \(-\) \(+\) \(q+(-\beta _{1}+\beta _{2})q^{3}+(2-\beta _{2}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(164))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(164)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 2}\)