Properties

Label 64.3.f
Level $64$
Weight $3$
Character orbit 64.f
Rep. character $\chi_{64}(15,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 64.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(64, [\chi])\).

Total New Old
Modular forms 40 10 30
Cusp forms 24 6 18
Eisenstein series 16 4 12

Trace form

\( 6q + 2q^{3} - 2q^{5} + 4q^{7} + O(q^{10}) \) \( 6q + 2q^{3} - 2q^{5} + 4q^{7} + 18q^{11} - 2q^{13} - 4q^{17} - 30q^{19} - 20q^{21} - 60q^{23} - 64q^{27} - 18q^{29} - 4q^{33} + 100q^{35} + 46q^{37} + 196q^{39} + 114q^{43} + 66q^{45} - 46q^{49} - 156q^{51} + 78q^{53} - 252q^{55} - 206q^{59} + 30q^{61} + 12q^{65} + 226q^{67} - 116q^{69} + 260q^{71} + 238q^{75} - 212q^{77} + 86q^{81} - 318q^{83} - 212q^{85} - 444q^{87} - 188q^{91} - 32q^{93} - 4q^{97} + 226q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
64.3.f.a \(6\) \(1.744\) 6.0.399424.1 None \(0\) \(2\) \(-2\) \(4\) \(q-\beta _{5}q^{3}+(-1-\beta _{1}-\beta _{3}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)