Properties

Label 64.24.a
Level $64$
Weight $24$
Character orbit 64.a
Rep. character $\chi_{64}(1,\cdot)$
Character field $\Q$
Dimension $45$
Newform subspaces $15$
Sturm bound $192$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 64.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(192\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(64))\).

Total New Old
Modular forms 190 47 143
Cusp forms 178 45 133
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.
\(+\)\(23\)
\(-\)\(22\)

Trace form

\( 45q + 2q^{5} + 1349385563185q^{9} + O(q^{10}) \) \( 45q + 2q^{5} + 1349385563185q^{9} + 14679969102058q^{13} - 112605054449254q^{17} - 2816606854453696q^{21} + 105092127635497067q^{25} + 40182344820854170q^{29} + 260763942015821088q^{33} - 3695983292865254398q^{37} - 423812055285736334q^{41} - 35506741043187658710q^{45} + 152483020894736533909q^{49} - 243471567206378773166q^{53} + 129888226131192780000q^{57} + 1404185762766222462618q^{61} - 752271782548128529884q^{65} - 1600174754769361596736q^{69} - 519127924113046457854q^{73} - 6333175115321920567104q^{77} + 50636703660686542572901q^{81} - 16258801490543646978172q^{85} - 6125289963067125364814q^{89} + 151248897441191345975552q^{93} + 66355999775620624191818q^{97} + O(q^{100}) \)

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(64))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
64.24.a.a \(1\) \(214.531\) \(\Q\) None \(0\) \(-505908\) \(90135570\) \(-6872255096\) \(-\) \(q-505908q^{3}+90135570q^{5}-6872255096q^{7}+\cdots\)
64.24.a.b \(1\) \(214.531\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(206464378\) \(0\) \(-\) \(q+206464378q^{5}-3^{23}q^{9}-7436301651582q^{13}+\cdots\)
64.24.a.c \(1\) \(214.531\) \(\Q\) None \(0\) \(505908\) \(90135570\) \(6872255096\) \(+\) \(q+505908q^{3}+90135570q^{5}+6872255096q^{7}+\cdots\)
64.24.a.d \(2\) \(214.531\) \(\Q(\sqrt{144169}) \) None \(0\) \(-339480\) \(-73069020\) \(-1359184400\) \(+\) \(q+(-169740-3\beta )q^{3}+(-36534510+\cdots)q^{5}+\cdots\)
64.24.a.e \(2\) \(214.531\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(-170520\) \(92266020\) \(192083440\) \(+\) \(q+(-85260-\beta )q^{3}+(46133010+540\beta )q^{5}+\cdots\)
64.24.a.f \(2\) \(214.531\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(170520\) \(92266020\) \(-192083440\) \(-\) \(q+(85260-\beta )q^{3}+(46133010-540\beta )q^{5}+\cdots\)
64.24.a.g \(2\) \(214.531\) \(\Q(\sqrt{144169}) \) None \(0\) \(339480\) \(-73069020\) \(1359184400\) \(-\) \(q+(169740-3\beta )q^{3}+(-36534510+\cdots)q^{5}+\cdots\)
64.24.a.h \(3\) \(214.531\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-213948\) \(-95628618\) \(8647912920\) \(-\) \(q+(-71316-\beta _{1})q^{3}+(-31876206+\cdots)q^{5}+\cdots\)
64.24.a.i \(3\) \(214.531\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-32708\) \(-31480650\) \(993025320\) \(+\) \(q+(-10903-\beta _{1})q^{3}+(-10493544+\cdots)q^{5}+\cdots\)
64.24.a.j \(3\) \(214.531\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(32708\) \(-31480650\) \(-993025320\) \(-\) \(q+(10903+\beta _{1})q^{3}+(-10493544+\cdots)q^{5}+\cdots\)
64.24.a.k \(3\) \(214.531\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(213948\) \(-95628618\) \(-8647912920\) \(+\) \(q+(71316+\beta _{1})q^{3}+(-31876206+\cdots)q^{5}+\cdots\)
64.24.a.l \(4\) \(214.531\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(-19990040\) \(0\) \(-\) \(q+\beta _{1}q^{3}+(-4997510-5\beta _{2})q^{5}+\cdots\)
64.24.a.m \(6\) \(214.531\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-483920\) \(6100380\) \(-347289696\) \(+\) \(q+(-80653+\beta _{1})q^{3}+(1016775+135\beta _{1}+\cdots)q^{5}+\cdots\)
64.24.a.n \(6\) \(214.531\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(-163121700\) \(0\) \(-\) \(q+\beta _{1}q^{3}+(-27186950-\beta _{2})q^{5}+\cdots\)
64.24.a.o \(6\) \(214.531\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(483920\) \(6100380\) \(347289696\) \(+\) \(q+(80653-\beta _{1})q^{3}+(1016775+135\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(64))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(64)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)