Properties

Label 164.2.f
Level $164$
Weight $2$
Character orbit 164.f
Rep. character $\chi_{164}(9,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $1$
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.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(42\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(164, [\chi])\).

Total New Old
Modular forms 48 6 42
Cusp forms 36 6 30
Eisenstein series 12 0 12

Trace form

\( 6q + 2q^{3} + O(q^{10}) \) \( 6q + 2q^{3} - 4q^{11} - 2q^{13} - 2q^{15} - 2q^{17} + 2q^{19} + 4q^{23} + 6q^{25} + 2q^{27} - 10q^{29} + 8q^{31} + 18q^{35} - 36q^{37} + 6q^{41} - 20q^{45} - 26q^{47} + 12q^{51} - 14q^{53} - 6q^{55} - 24q^{57} - 4q^{59} + 18q^{63} + 20q^{65} + 16q^{67} + 8q^{69} + 26q^{71} - 10q^{75} - 2q^{79} + 38q^{81} + 36q^{83} + 44q^{85} + 14q^{89} - 28q^{93} - 26q^{95} - 6q^{97} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(164, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
164.2.f.a \(6\) \(1.310\) 6.0.5089536.1 None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(164, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(164, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 2}\)