Properties

Label 64.22.a
Level $64$
Weight $22$
Character orbit 64.a
Rep. character $\chi_{64}(1,\cdot)$
Character field $\Q$
Dimension $41$
Newform subspaces $17$
Sturm bound $176$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 64.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(176\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(64))\).

Total New Old
Modular forms 174 43 131
Cusp forms 162 41 121
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
\(+\)\(20\)
\(-\)\(21\)

Trace form

\( 41 q + 2 q^{5} + 135984591637 q^{9} + O(q^{10}) \) \( 41 q + 2 q^{5} + 135984591637 q^{9} - 1065395863654 q^{13} + 3481428994002 q^{17} + 132761067402368 q^{21} + 3807066340697127 q^{25} - 2433173450216598 q^{29} - 10718205122066112 q^{33} - 17830227570674174 q^{37} + 2550812783630522 q^{41} + 827402995178917914 q^{45} + 2792729320416420033 q^{49} + 2140956801021598770 q^{53} - 3378567006828484416 q^{57} - 7508615876911824022 q^{61} - 6125468142667127532 q^{65} - 35904133933074186880 q^{69} - 5771745784109926806 q^{73} + 214596272327840298368 q^{77} + 418629249161332174801 q^{81} - 65877839254108777212 q^{85} + 359902412185241718330 q^{89} - 1367800221219678191104 q^{93} - 200185457171576537182 q^{97} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(64))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
64.22.a.a 64.a 1.a $1$ $178.866$ \(\Q\) None \(0\) \(-128844\) \(-21640950\) \(768078808\) $-$ $\mathrm{SU}(2)$ \(q-128844q^{3}-21640950q^{5}+768078808q^{7}+\cdots\)
64.22.a.b 64.a 1.a $1$ $178.866$ \(\Q\) None \(0\) \(-71604\) \(28693770\) \(-853202392\) $+$ $\mathrm{SU}(2)$ \(q-71604q^{3}+28693770q^{5}-853202392q^{7}+\cdots\)
64.22.a.c 64.a 1.a $1$ $178.866$ \(\Q\) None \(0\) \(-59316\) \(-4975350\) \(1427425832\) $+$ $\mathrm{SU}(2)$ \(q-59316q^{3}-4975350q^{5}+1427425832q^{7}+\cdots\)
64.22.a.d 64.a 1.a $1$ $178.866$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-13398638\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-13398638q^{5}-3^{21}q^{9}-970515066006q^{13}+\cdots\)
64.22.a.e 64.a 1.a $1$ $178.866$ \(\Q\) None \(0\) \(59316\) \(-4975350\) \(-1427425832\) $-$ $\mathrm{SU}(2)$ \(q+59316q^{3}-4975350q^{5}-1427425832q^{7}+\cdots\)
64.22.a.f 64.a 1.a $1$ $178.866$ \(\Q\) None \(0\) \(71604\) \(28693770\) \(853202392\) $-$ $\mathrm{SU}(2)$ \(q+71604q^{3}+28693770q^{5}+853202392q^{7}+\cdots\)
64.22.a.g 64.a 1.a $1$ $178.866$ \(\Q\) None \(0\) \(128844\) \(-21640950\) \(-768078808\) $+$ $\mathrm{SU}(2)$ \(q+128844q^{3}-21640950q^{5}-768078808q^{7}+\cdots\)
64.22.a.h 64.a 1.a $2$ $178.866$ \(\Q(\sqrt{358549}) \) None \(0\) \(-105432\) \(-2108140\) \(-444771792\) $-$ $\mathrm{SU}(2)$ \(q+(-52716-\beta )q^{3}+(-1054070+\cdots)q^{5}+\cdots\)
64.22.a.i 64.a 1.a $2$ $178.866$ \(\Q(\sqrt{2161}) \) None \(0\) \(-65640\) \(-13689324\) \(-260508080\) $+$ $\mathrm{SU}(2)$ \(q+(-32820-\beta )q^{3}+(-6844662+\cdots)q^{5}+\cdots\)
64.22.a.j 64.a 1.a $2$ $178.866$ \(\Q(\sqrt{2161}) \) None \(0\) \(65640\) \(-13689324\) \(260508080\) $-$ $\mathrm{SU}(2)$ \(q+(32820-\beta )q^{3}+(-6844662+204\beta )q^{5}+\cdots\)
64.22.a.k 64.a 1.a $2$ $178.866$ \(\Q(\sqrt{358549}) \) None \(0\) \(105432\) \(-2108140\) \(444771792\) $+$ $\mathrm{SU}(2)$ \(q+(52716-\beta )q^{3}+(-1054070+20\beta )q^{5}+\cdots\)
64.22.a.l 64.a 1.a $3$ $178.866$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-96764\) \(24111774\) \(295988280\) $+$ $\mathrm{SU}(2)$ \(q+(-32255+\beta _{1})q^{3}+(8037261-9\beta _{1}+\cdots)q^{5}+\cdots\)
64.22.a.m 64.a 1.a $3$ $178.866$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(96764\) \(24111774\) \(-295988280\) $-$ $\mathrm{SU}(2)$ \(q+(32255-\beta _{1})q^{3}+(8037261-9\beta _{1}+\cdots)q^{5}+\cdots\)
64.22.a.n 64.a 1.a $4$ $178.866$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(37124680\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(9281170+115\beta _{2})q^{5}+\cdots\)
64.22.a.o 64.a 1.a $5$ $178.866$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-23144\) \(-18311174\) \(63978640\) $+$ $\mathrm{SU}(2)$ \(q+(-4629+\beta _{1})q^{3}+(-3662238+\cdots)q^{5}+\cdots\)
64.22.a.p 64.a 1.a $5$ $178.866$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(23144\) \(-18311174\) \(-63978640\) $+$ $\mathrm{SU}(2)$ \(q+(4629-\beta _{1})q^{3}+(-3662238+14\beta _{1}+\cdots)q^{5}+\cdots\)
64.22.a.q 64.a 1.a $6$ $178.866$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(-7887252\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1314542+\beta _{2})q^{5}+(-1762\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(64))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(64)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)