Properties

Label 8016.2.a
Level 8016
Weight 2
Character orbit a
Rep. character \(\chi_{8016}(1,\cdot)\)
Character field \(\Q\)
Dimension 166
Newforms 33
Sturm bound 2688
Trace bound 11

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)
Character field: \(\Q\)
Newforms: \( 33 \)
Sturm bound: \(2688\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8016))\).

Total New Old
Modular forms 1356 166 1190
Cusp forms 1333 166 1167
Eisenstein series 23 0 23

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

\(2\)\(3\)\(167\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(19\)
\(+\)\(+\)\(-\)\(-\)\(23\)
\(+\)\(-\)\(+\)\(-\)\(22\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(23\)
\(-\)\(+\)\(-\)\(+\)\(19\)
\(-\)\(-\)\(+\)\(+\)\(19\)
\(-\)\(-\)\(-\)\(-\)\(23\)
Plus space\(+\)\(75\)
Minus space\(-\)\(91\)

Trace form

\(166q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 166q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(166q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 166q^{9} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 170q^{25} \) \(\mathstrut -\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut +\mathstrut 166q^{49} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 24q^{55} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 28q^{67} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut -\mathstrut 14q^{75} \) \(\mathstrut -\mathstrut 16q^{77} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 166q^{81} \) \(\mathstrut -\mathstrut 24q^{83} \) \(\mathstrut +\mathstrut 24q^{85} \) \(\mathstrut +\mathstrut 12q^{87} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8016))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 167
8016.2.a.a \(1\) \(64.008\) \(\Q\) None \(0\) \(-1\) \(-3\) \(3\) \(-\) \(+\) \(-\) \(q-q^{3}-3q^{5}+3q^{7}+q^{9}-6q^{13}+\cdots\)
8016.2.a.b \(1\) \(64.008\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
8016.2.a.c \(1\) \(64.008\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
8016.2.a.d \(1\) \(64.008\) \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{3}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
8016.2.a.e \(1\) \(64.008\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+q^{9}+2q^{17}+8q^{19}+4q^{23}+\cdots\)
8016.2.a.f \(1\) \(64.008\) \(\Q\) None \(0\) \(-1\) \(2\) \(4\) \(-\) \(+\) \(+\) \(q-q^{3}+2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
8016.2.a.g \(1\) \(64.008\) \(\Q\) None \(0\) \(1\) \(-4\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{3}-4q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
8016.2.a.h \(1\) \(64.008\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{9}-4q^{13}+6q^{17}-4q^{23}+\cdots\)
8016.2.a.i \(1\) \(64.008\) \(\Q\) None \(0\) \(1\) \(1\) \(3\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{5}+3q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8016.2.a.j \(1\) \(64.008\) \(\Q\) None \(0\) \(1\) \(3\) \(-3\) \(-\) \(-\) \(+\) \(q+q^{3}+3q^{5}-3q^{7}+q^{9}-6q^{11}+\cdots\)
8016.2.a.k \(2\) \(64.008\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+(-2+\beta )q^{5}+2\beta q^{7}+q^{9}+\cdots\)
8016.2.a.l \(3\) \(64.008\) 3.3.148.1 None \(0\) \(3\) \(-3\) \(5\) \(-\) \(-\) \(+\) \(q+q^{3}+(-1+\beta _{2})q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
8016.2.a.m \(3\) \(64.008\) 3.3.1300.1 None \(0\) \(3\) \(3\) \(-1\) \(-\) \(-\) \(-\) \(q+q^{3}+(1-\beta _{1})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
8016.2.a.n \(3\) \(64.008\) 3.3.148.1 None \(0\) \(3\) \(6\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}+(2-\beta _{2})q^{5}+(2-2\beta _{1})q^{7}+q^{9}+\cdots\)
8016.2.a.o \(4\) \(64.008\) 4.4.2777.1 None \(0\) \(4\) \(5\) \(-1\) \(-\) \(-\) \(-\) \(q+q^{3}+(1-\beta _{1})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots\)
8016.2.a.p \(5\) \(64.008\) 5.5.36497.1 None \(0\) \(-5\) \(-9\) \(4\) \(-\) \(+\) \(+\) \(q-q^{3}+(-2-\beta _{1}-\beta _{2}-\beta _{4})q^{5}+(1+\cdots)q^{7}+\cdots\)
8016.2.a.q \(5\) \(64.008\) 5.5.161121.1 None \(0\) \(-5\) \(-7\) \(2\) \(-\) \(+\) \(-\) \(q-q^{3}+(-1-\beta _{3}-\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
8016.2.a.r \(5\) \(64.008\) 5.5.11256624.1 None \(0\) \(-5\) \(-1\) \(-9\) \(-\) \(+\) \(-\) \(q-q^{3}+\beta _{2}q^{5}+(-2+\beta _{4})q^{7}+q^{9}+\cdots\)
8016.2.a.s \(5\) \(64.008\) 5.5.284897.1 None \(0\) \(-5\) \(1\) \(4\) \(+\) \(+\) \(+\) \(q-q^{3}+(-\beta _{3}+\beta _{4})q^{5}+(1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
8016.2.a.t \(5\) \(64.008\) 5.5.149169.1 None \(0\) \(5\) \(-3\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}+(-\beta _{1}+\beta _{3}-\beta _{4})q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots\)
8016.2.a.u \(5\) \(64.008\) 5.5.38569.1 None \(0\) \(5\) \(-1\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+(\beta _{1}+\beta _{4})q^{5}+(1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
8016.2.a.v \(7\) \(64.008\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-7\) \(5\) \(-7\) \(-\) \(+\) \(+\) \(q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
8016.2.a.w \(7\) \(64.008\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(7\) \(-3\) \(-8\) \(+\) \(-\) \(-\) \(q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots\)
8016.2.a.x \(8\) \(64.008\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-8\) \(7\) \(4\) \(-\) \(+\) \(-\) \(q-q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
8016.2.a.y \(8\) \(64.008\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(0\) \(1\) \(+\) \(-\) \(+\) \(q+q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
8016.2.a.z \(8\) \(64.008\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}+(\beta _{1}+\beta _{2}-\beta _{5})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
8016.2.a.ba \(9\) \(64.008\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(-6\) \(11\) \(+\) \(+\) \(-\) \(q-q^{3}+(-1+\beta _{1})q^{5}+(2-\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots\)
8016.2.a.bb \(9\) \(64.008\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(9\) \(-2\) \(-\) \(+\) \(+\) \(q-q^{3}+(1-\beta _{1})q^{5}+\beta _{6}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8016.2.a.bc \(9\) \(64.008\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(9\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta _{1}q^{5}+(\beta _{3}+\beta _{6})q^{7}+q^{9}+\cdots\)
8016.2.a.bd \(10\) \(64.008\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(10\) \(-10\) \(-1\) \(+\) \(-\) \(-\) \(q+q^{3}+(-1-\beta _{1})q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
8016.2.a.be \(11\) \(64.008\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(11\) \(10\) \(1\) \(+\) \(-\) \(+\) \(q+q^{3}+(1-\beta _{1})q^{5}-\beta _{3}q^{7}+q^{9}+\beta _{10}q^{11}+\cdots\)
8016.2.a.bf \(12\) \(64.008\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-12\) \(4\) \(-11\) \(+\) \(+\) \(+\) \(q-q^{3}+\beta _{1}q^{5}+(-1+\beta _{9})q^{7}+q^{9}+\cdots\)
8016.2.a.bg \(13\) \(64.008\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-13\) \(2\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{3}+\beta _{1}q^{5}+\beta _{9}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(501))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(668))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1002))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2004))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4008))\)\(^{\oplus 2}\)