Properties

Label 64.20.a
Level $64$
Weight $20$
Character orbit 64.a
Rep. character $\chi_{64}(1,\cdot)$
Character field $\Q$
Dimension $37$
Newform subspaces $17$
Sturm bound $160$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 64.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(160\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(64))\).

Total New Old
Modular forms 158 39 119
Cusp forms 146 37 109
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.
\(+\)\(19\)
\(-\)\(18\)

Trace form

\( 37q + 2q^{5} + 13559717113q^{9} + O(q^{10}) \) \( 37q + 2q^{5} + 13559717113q^{9} + 51826863306q^{13} + 28242853386q^{17} + 4583626701248q^{21} + 107902434751587q^{25} + 108453057658554q^{29} + 370762863890400q^{33} + 2699870505305602q^{37} + 3452822229087362q^{41} - 17514471298184310q^{45} + 50480821535223917q^{49} - 9738205886287854q^{53} - 25419604822759392q^{57} + 9182008383285178q^{61} - 130435657684110204q^{65} + 569547136460925248q^{69} + 216554693256734546q^{73} - 1607739728743220416q^{77} + 6255293395795413565q^{81} + 6339227636564425348q^{85} - 6475623728168618430q^{89} - 20001819644368417024q^{93} + 11782117141644799738q^{97} + O(q^{100}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(64))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
64.20.a.a \(1\) \(146.443\) \(\Q\) None \(0\) \(-53028\) \(5556930\) \(44496424\) \(-\) \(q-53028q^{3}+5556930q^{5}+44496424q^{7}+\cdots\)
64.20.a.b \(1\) \(146.443\) \(\Q\) None \(0\) \(-50652\) \(2377410\) \(-16917544\) \(+\) \(q-50652q^{3}+2377410q^{5}-16917544q^{7}+\cdots\)
64.20.a.c \(1\) \(146.443\) \(\Q\) None \(0\) \(-13092\) \(-6546750\) \(-96674264\) \(-\) \(q-13092q^{3}-6546750q^{5}-96674264q^{7}+\cdots\)
64.20.a.d \(1\) \(146.443\) \(\Q\) None \(0\) \(-36\) \(196290\) \(35905576\) \(-\) \(q-6^{2}q^{3}+196290q^{5}+35905576q^{7}+\cdots\)
64.20.a.e \(1\) \(146.443\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-5042902\) \(0\) \(-\) \(q-5042902q^{5}-3^{19}q^{9}-13425142062q^{13}+\cdots\)
64.20.a.f \(1\) \(146.443\) \(\Q\) None \(0\) \(36\) \(196290\) \(-35905576\) \(+\) \(q+6^{2}q^{3}+196290q^{5}-35905576q^{7}+\cdots\)
64.20.a.g \(1\) \(146.443\) \(\Q\) None \(0\) \(13092\) \(-6546750\) \(96674264\) \(+\) \(q+13092q^{3}-6546750q^{5}+96674264q^{7}+\cdots\)
64.20.a.h \(1\) \(146.443\) \(\Q\) None \(0\) \(50652\) \(2377410\) \(16917544\) \(-\) \(q+50652q^{3}+2377410q^{5}+16917544q^{7}+\cdots\)
64.20.a.i \(1\) \(146.443\) \(\Q\) None \(0\) \(53028\) \(5556930\) \(-44496424\) \(+\) \(q+53028q^{3}+5556930q^{5}-44496424q^{7}+\cdots\)
64.20.a.j \(2\) \(146.443\) \(\Q(\sqrt{1453}) \) None \(0\) \(-27912\) \(-1226620\) \(-88510512\) \(-\) \(q+(-13956-\beta )q^{3}+(-613310-44\beta )q^{5}+\cdots\)
64.20.a.k \(2\) \(146.443\) \(\Q(\sqrt{1453}) \) None \(0\) \(27912\) \(-1226620\) \(88510512\) \(+\) \(q+(13956-\beta )q^{3}+(-613310+44\beta )q^{5}+\cdots\)
64.20.a.l \(3\) \(146.443\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-23732\) \(-2140218\) \(55851720\) \(+\) \(q+(-7911+\beta _{1})q^{3}+(-713429+70\beta _{1}+\cdots)q^{5}+\cdots\)
64.20.a.m \(3\) \(146.443\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(23732\) \(-2140218\) \(-55851720\) \(-\) \(q+(7911-\beta _{1})q^{3}+(-713429+70\beta _{1}+\cdots)q^{5}+\cdots\)
64.20.a.n \(4\) \(146.443\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(-4924760\) \(0\) \(-\) \(q-\beta _{1}q^{3}+(-1231190-\beta _{2})q^{5}+(-830\beta _{1}+\cdots)q^{7}+\cdots\)
64.20.a.o \(4\) \(146.443\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(5322920\) \(0\) \(-\) \(q-\beta _{1}q^{3}+(1330730-5\beta _{2})q^{5}+(941\beta _{1}+\cdots)q^{7}+\cdots\)
64.20.a.p \(5\) \(146.443\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-6424\) \(4105330\) \(-107158480\) \(+\) \(q+(-1285-\beta _{1})q^{3}+(821058-39\beta _{1}+\cdots)q^{5}+\cdots\)
64.20.a.q \(5\) \(146.443\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(6424\) \(4105330\) \(107158480\) \(+\) \(q+(1285+\beta _{1})q^{3}+(821058-39\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(64))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_0(64)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)