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

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

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

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