Properties

Label 8024.2.a
Level 8024
Weight 2
Character orbit a
Rep. character \(\chi_{8024}(1,\cdot)\)
Character field \(\Q\)
Dimension 232
Newforms 29
Sturm bound 2160
Trace bound 7

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Defining parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)
Character field: \(\Q\)
Newforms: \( 29 \)
Sturm bound: \(2160\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8024))\).

Total New Old
Modular forms 1088 232 856
Cusp forms 1073 232 841
Eisenstein series 15 0 15

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

\(2\)\(17\)\(59\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(28\)
\(+\)\(+\)\(-\)\(-\)\(31\)
\(+\)\(-\)\(+\)\(-\)\(30\)
\(+\)\(-\)\(-\)\(+\)\(27\)
\(-\)\(+\)\(+\)\(-\)\(34\)
\(-\)\(+\)\(-\)\(+\)\(25\)
\(-\)\(-\)\(+\)\(+\)\(24\)
\(-\)\(-\)\(-\)\(-\)\(33\)
Plus space\(+\)\(104\)
Minus space\(-\)\(128\)

Trace form

\(232q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 224q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(232q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 224q^{9} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 232q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut +\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 24q^{41} \) \(\mathstrut +\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 44q^{45} \) \(\mathstrut -\mathstrut 24q^{47} \) \(\mathstrut +\mathstrut 216q^{49} \) \(\mathstrut +\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 8q^{53} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 32q^{57} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 32q^{67} \) \(\mathstrut +\mathstrut 40q^{69} \) \(\mathstrut -\mathstrut 56q^{71} \) \(\mathstrut -\mathstrut 8q^{73} \) \(\mathstrut -\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 224q^{81} \) \(\mathstrut -\mathstrut 40q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 40q^{89} \) \(\mathstrut +\mathstrut 88q^{91} \) \(\mathstrut -\mathstrut 8q^{93} \) \(\mathstrut -\mathstrut 16q^{95} \) \(\mathstrut +\mathstrut 32q^{97} \) \(\mathstrut -\mathstrut 40q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 17 59
8024.2.a.a \(1\) \(64.072\) \(\Q\) None \(0\) \(-3\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(q-3q^{3}+q^{5}-q^{7}+6q^{9}+4q^{13}+\cdots\)
8024.2.a.b \(1\) \(64.072\) \(\Q\) None \(0\) \(-1\) \(-3\) \(-3\) \(-\) \(+\) \(-\) \(q-q^{3}-3q^{5}-3q^{7}-2q^{9}-4q^{11}+\cdots\)
8024.2.a.c \(1\) \(64.072\) \(\Q\) None \(0\) \(-1\) \(-3\) \(1\) \(+\) \(-\) \(-\) \(q-q^{3}-3q^{5}+q^{7}-2q^{9}-4q^{11}+\cdots\)
8024.2.a.d \(1\) \(64.072\) \(\Q\) None \(0\) \(-1\) \(-3\) \(3\) \(-\) \(+\) \(+\) \(q-q^{3}-3q^{5}+3q^{7}-2q^{9}+2q^{11}+\cdots\)
8024.2.a.e \(1\) \(64.072\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{3}-q^{5}-q^{7}-2q^{9}-6q^{11}-4q^{13}+\cdots\)
8024.2.a.f \(1\) \(64.072\) \(\Q\) None \(0\) \(-1\) \(2\) \(-4\) \(+\) \(-\) \(+\) \(q-q^{3}+2q^{5}-4q^{7}-2q^{9}+6q^{11}+\cdots\)
8024.2.a.g \(1\) \(64.072\) \(\Q\) None \(0\) \(-1\) \(3\) \(1\) \(+\) \(-\) \(-\) \(q-q^{3}+3q^{5}+q^{7}-2q^{9}-4q^{11}+\cdots\)
8024.2.a.h \(1\) \(64.072\) \(\Q\) None \(0\) \(0\) \(-2\) \(4\) \(+\) \(+\) \(-\) \(q-2q^{5}+4q^{7}-3q^{9}+2q^{11}+2q^{13}+\cdots\)
8024.2.a.i \(1\) \(64.072\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(+\) \(+\) \(+\) \(q+2q^{5}-3q^{9}+2q^{11}-6q^{13}-q^{17}+\cdots\)
8024.2.a.j \(1\) \(64.072\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{5}-q^{7}-2q^{9}+4q^{11}+2q^{13}+\cdots\)
8024.2.a.k \(1\) \(64.072\) \(\Q\) None \(0\) \(2\) \(-4\) \(4\) \(-\) \(-\) \(-\) \(q+2q^{3}-4q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots\)
8024.2.a.l \(1\) \(64.072\) \(\Q\) None \(0\) \(2\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(q+2q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
8024.2.a.m \(1\) \(64.072\) \(\Q\) None \(0\) \(2\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(q+2q^{3}+2q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots\)
8024.2.a.n \(1\) \(64.072\) \(\Q\) None \(0\) \(3\) \(-1\) \(3\) \(+\) \(-\) \(+\) \(q+3q^{3}-q^{5}+3q^{7}+6q^{9}+2q^{11}+\cdots\)
8024.2.a.o \(1\) \(64.072\) \(\Q\) None \(0\) \(3\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(q+3q^{3}+q^{5}-q^{7}+6q^{9}-6q^{11}+\cdots\)
8024.2.a.p \(2\) \(64.072\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-3\) \(-3\) \(-\) \(-\) \(+\) \(q+\beta q^{3}+(-2+\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
8024.2.a.q \(2\) \(64.072\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-1\) \(-3\) \(-\) \(-\) \(+\) \(q+\beta q^{3}-\beta q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
8024.2.a.r \(2\) \(64.072\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(q+q^{3}+(-2-\beta )q^{5}+\beta q^{7}-2q^{9}+\cdots\)
8024.2.a.s \(3\) \(64.072\) 3.3.229.1 None \(0\) \(-1\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
8024.2.a.t \(3\) \(64.072\) 3.3.229.1 None \(0\) \(0\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
8024.2.a.u \(3\) \(64.072\) 3.3.568.1 None \(0\) \(3\) \(4\) \(2\) \(+\) \(-\) \(+\) \(q+q^{3}+(1-\beta _{2})q^{5}+(1-\beta _{1})q^{7}-2q^{9}+\cdots\)
8024.2.a.v \(18\) \(64.072\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(9\) \(2\) \(11\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+\beta _{3}q^{5}+(1-\beta _{6})q^{7}+\cdots\)
8024.2.a.w \(20\) \(64.072\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-2\) \(-2\) \(5\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{3}+\beta _{17}q^{5}+\beta _{15}q^{7}+\beta _{2}q^{9}+\cdots\)
8024.2.a.x \(22\) \(64.072\) None \(0\) \(-3\) \(3\) \(0\) \(-\) \(+\) \(-\)
8024.2.a.y \(23\) \(64.072\) None \(0\) \(-6\) \(0\) \(-1\) \(+\) \(+\) \(+\)
8024.2.a.z \(24\) \(64.072\) None \(0\) \(-5\) \(-7\) \(-12\) \(+\) \(-\) \(-\)
8024.2.a.ba \(30\) \(64.072\) None \(0\) \(4\) \(2\) \(3\) \(+\) \(+\) \(-\)
8024.2.a.bb \(32\) \(64.072\) None \(0\) \(0\) \(8\) \(-3\) \(-\) \(-\) \(-\)
8024.2.a.bc \(33\) \(64.072\) None \(0\) \(-3\) \(3\) \(0\) \(-\) \(+\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(236))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(472))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1003))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2006))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4012))\)\(^{\oplus 2}\)