Properties

Label 8036.2.a
Level 8036
Weight 2
Character orbit a
Rep. character \(\chi_{8036}(1,\cdot)\)
Character field \(\Q\)
Dimension 136
Newforms 20
Sturm bound 2352
Trace bound 13

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)
Character field: \(\Q\)
Newforms: \( 20 \)
Sturm bound: \(2352\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8036))\).

Total New Old
Modular forms 1200 136 1064
Cusp forms 1153 136 1017
Eisenstein series 47 0 47

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

\(2\)\(7\)\(41\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(37\)
\(-\)\(+\)\(-\)\(+\)\(29\)
\(-\)\(-\)\(+\)\(+\)\(29\)
\(-\)\(-\)\(-\)\(-\)\(41\)
Plus space\(+\)\(58\)
Minus space\(-\)\(78\)

Trace form

\(136q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 132q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(136q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 132q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 140q^{25} \) \(\mathstrut +\mathstrut 14q^{27} \) \(\mathstrut -\mathstrut 4q^{29} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 32q^{37} \) \(\mathstrut +\mathstrut 36q^{39} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 28q^{43} \) \(\mathstrut +\mathstrut 14q^{47} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 8q^{53} \) \(\mathstrut +\mathstrut 26q^{55} \) \(\mathstrut +\mathstrut 36q^{57} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 16q^{67} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut +\mathstrut 14q^{71} \) \(\mathstrut +\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut +\mathstrut 38q^{79} \) \(\mathstrut +\mathstrut 112q^{81} \) \(\mathstrut +\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 12q^{85} \) \(\mathstrut +\mathstrut 12q^{89} \) \(\mathstrut +\mathstrut 40q^{93} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 12q^{97} \) \(\mathstrut -\mathstrut 30q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8036))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 41
8036.2.a.a \(1\) \(64.168\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}-q^{5}-2q^{9}-5q^{11}-2q^{13}+\cdots\)
8036.2.a.b \(1\) \(64.168\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-q^{5}-2q^{9}+3q^{11}+2q^{13}+\cdots\)
8036.2.a.c \(1\) \(64.168\) \(\Q\) None \(0\) \(-1\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q-q^{3}+3q^{5}-2q^{9}+3q^{11}+4q^{13}+\cdots\)
8036.2.a.d \(1\) \(64.168\) \(\Q\) None \(0\) \(1\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(q+q^{3}-3q^{5}-2q^{9}+3q^{11}-4q^{13}+\cdots\)
8036.2.a.e \(1\) \(64.168\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-2q^{9}-5q^{11}+2q^{13}+\cdots\)
8036.2.a.f \(1\) \(64.168\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-2q^{9}+3q^{11}-2q^{13}+\cdots\)
8036.2.a.g \(2\) \(64.168\) \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{3}+(1+\beta )q^{5}+(1+3\beta )q^{9}+\cdots\)
8036.2.a.h \(3\) \(64.168\) \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{3}+(2\beta _{1}-2\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
8036.2.a.i \(4\) \(64.168\) 4.4.25808.1 None \(0\) \(-2\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(q+(\beta _{1}-\beta _{2})q^{3}+(-2+\beta _{2}-\beta _{3})q^{5}+\cdots\)
8036.2.a.j \(5\) \(64.168\) 5.5.1935333.1 None \(0\) \(-2\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
8036.2.a.k \(5\) \(64.168\) 5.5.287349.1 None \(0\) \(-2\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{2}q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+(\beta _{2}+\beta _{4})q^{9}+\cdots\)
8036.2.a.l \(5\) \(64.168\) 5.5.470117.1 None \(0\) \(2\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
8036.2.a.m \(8\) \(64.168\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}+\beta _{5}q^{5}+(1+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
8036.2.a.n \(8\) \(64.168\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}-\beta _{5}q^{5}+(1+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
8036.2.a.o \(10\) \(64.168\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-2\) \(-4\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(1+\beta _{2}+\beta _{3})q^{9}+\cdots\)
8036.2.a.p \(10\) \(64.168\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(2\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{2}+\beta _{3})q^{9}+\cdots\)
8036.2.a.q \(15\) \(64.168\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(-1\) \(3\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(2+\beta _{2})q^{9}+(1-\beta _{3}+\cdots)q^{11}+\cdots\)
8036.2.a.r \(15\) \(64.168\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(1\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(2+\beta _{2})q^{9}+(1-\beta _{3}+\cdots)q^{11}+\cdots\)
8036.2.a.s \(20\) \(64.168\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-4\) \(-8\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}+\beta _{11}q^{5}+(1+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
8036.2.a.t \(20\) \(64.168\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(4\) \(8\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}-\beta _{11}q^{5}+(1+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8036))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8036)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1148))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2009))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4018))\)\(^{\oplus 2}\)