Properties

Label 64.4.a
Level $64$
Weight $4$
Character orbit 64.a
Rep. character $\chi_{64}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
Sturm bound $32$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 64.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(64))\).

Total New Old
Modular forms 30 7 23
Cusp forms 18 5 13
Eisenstein series 12 2 10

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

\(2\)Dim
\(+\)\(3\)
\(-\)\(2\)

Trace form

\( 5 q + 2 q^{5} + 25 q^{9} + O(q^{10}) \) \( 5 q + 2 q^{5} + 25 q^{9} + 74 q^{13} - 54 q^{17} - 64 q^{21} + 67 q^{25} - 198 q^{29} - 288 q^{33} - 510 q^{37} + 194 q^{41} + 1290 q^{45} - 51 q^{49} + 786 q^{53} + 288 q^{57} - 1990 q^{61} + 516 q^{65} - 1216 q^{69} + 146 q^{73} + 3392 q^{77} - 611 q^{81} + 1668 q^{85} - 894 q^{89} - 6400 q^{93} - 582 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(64))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
64.4.a.a 64.a 1.a $1$ $3.776$ \(\Q\) None 32.4.a.a \(0\) \(-8\) \(10\) \(16\) $+$ $\mathrm{SU}(2)$ \(q-8q^{3}+10q^{5}+2^{4}q^{7}+37q^{9}+40q^{11}+\cdots\)
64.4.a.b 64.a 1.a $1$ $3.776$ \(\Q\) None 8.4.a.a \(0\) \(-4\) \(2\) \(-24\) $-$ $\mathrm{SU}(2)$ \(q-4q^{3}+2q^{5}-24q^{7}-11q^{9}-44q^{11}+\cdots\)
64.4.a.c 64.a 1.a $1$ $3.776$ \(\Q\) \(\Q(\sqrt{-1}) \) 32.4.a.b \(0\) \(0\) \(-22\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-22q^{5}-3^{3}q^{9}+18q^{13}-94q^{17}+\cdots\)
64.4.a.d 64.a 1.a $1$ $3.776$ \(\Q\) None 8.4.a.a \(0\) \(4\) \(2\) \(24\) $+$ $\mathrm{SU}(2)$ \(q+4q^{3}+2q^{5}+24q^{7}-11q^{9}+44q^{11}+\cdots\)
64.4.a.e 64.a 1.a $1$ $3.776$ \(\Q\) None 32.4.a.a \(0\) \(8\) \(10\) \(-16\) $+$ $\mathrm{SU}(2)$ \(q+8q^{3}+10q^{5}-2^{4}q^{7}+37q^{9}-40q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(64))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(64)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)